{"id":27850,"date":"2022-04-07T09:10:44","date_gmt":"2022-04-07T03:40:44","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=27850"},"modified":"2022-04-07T10:58:16","modified_gmt":"2022-04-07T05:28:16","slug":"big-ideas-math-answers-grade-7-chapter-9","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7-chapter-9\/","title":{"rendered":"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles"},"content":{"rendered":"<p>Get <b>Big Ideas Math Answer Key for Grade 7 Chapter 9 Geometric Shapes and Angles Pdf<\/b> here. We are providing free download links to all problems in the upcoming sections. You can understand the concept easily as we are explaining the concept with so many real-time examples. Candidates can improve their problem-solving skills and analytical thinking with the help of Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles.<\/p>\n<p>BIM Grade 7 Chapter 9 Geometric Shapes and Angles Answer Key pdf. Download all the pdf links from here for free of cost and kickstart your exam preparation. Follow the various concepts and solve as many problems as before going to the exam. We are providing the preparatory material for the candidates to score better marks in the exam. <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7\/\">Grade 7 Big Ideas Math Answers<\/a> is providing amazing tips and tricks in the next sections. Check it out!!<\/p>\n<h2>Big Ideas Math Book 7th Grade Answer Key 9 Geometric Shapes and Angles<\/h2>\n<p>If it is some theory, then you can easily learn it but if it is problematic, then you must have perfection and grip on the subject. Therefore, we are providing a lot of practice material with solutions. First, read the question and try to solve the problems without looking at the solutions. Then refer to the solution and know if it is correct or not. Also, check if it the easiest process or not. With the help of professionals and math experts, we gave the solution to the problems in the easiest methods.<\/p>\n<p>You need not be the expert in all the topics but you must check the easy topics like Geometric Shapes and Angles and prepare perfectly. These topics act as a scoring factor because they are easy to understand and solve. If you have any further doubts, go through <em><strong>Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles,<\/strong> y<\/em>ou will get a clear idea about every detail.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Geometric_Shapes_and_Angles_STEAM_Video\/Performance_Task\">Geometric Shapes and Angles STEAM Video\/Performance Task<\/a><\/li>\n<li><a href=\"#Geometric_Shapes_and_Angles_Getting_Ready_for_Chapter_9\">Geometric Shapes and Angles Getting Ready for Chapter 9<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Circle and Circumference<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.1_Circles_and_Circumference\">Lesson 9.1 Circles and Circumference<\/a><\/li>\n<li><a href=\"#Circles_and_Circumference_Homework_&amp;_Practice_9.1\">Circles and Circumference Homework &amp; Practice 9.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Areas of Circles<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.2_Areas_of_Circles\">Lesson 9.2 Areas of Circles<\/a><\/li>\n<li><a href=\"#Areas_of_Circles_Homework_&amp;_Practice_9.2\">Areas of Circles Homework &amp; Practice 9.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Perimeters and Areas of Composite Figures<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.3_Perimeters_and_Areas_of_Composite_Figures\">Lesson 9.3 Perimeters and Areas of Composite Figures<\/a><\/li>\n<li><a href=\"#Perimeters_and_Areas_of_Composite_Figures_Homework_&amp;_Practice_9.3\">Perimeters and Areas of Composite Figures Homework &amp; Practice 9.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Constructing Polygons<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.4_Constructing_Polygons\">Lesson 9.4 Constructing Polygons<\/a><\/li>\n<li><a href=\"#Constructing_Polygons_Homework_&amp;_Practice_9.4\">Constructing Polygons Homework &amp; Practice 9.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Finding Unknown Angle Measures<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_9.5_Finding_Unknown_Angle_Measures\">Lesson 9.5 Finding Unknown Angle Measures<\/a><\/li>\n<li><a href=\"#Finding_Unknown_Angle_Measures_Homework_&amp;_Practice_9.5\">Finding Unknown Angle Measures Homework &amp; Practice 9.5<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 9 &#8211; Geometric Shapes and Angles<\/strong><\/p>\n<ul>\n<li><a href=\"#Geometric_Shapes_and_Angles_Connecting_Concepts\">Geometric Shapes and Angles Connecting Concepts<\/a><\/li>\n<li><a href=\"#Geometric_Shapes_and_Angles_Chapter_Review\">Geometric Shapes and Angles Chapter Review<\/a><\/li>\n<li><a href=\"#Geometric_Shapes_and_Angles_Practice_Test\">Geometric Shapes and Angles Practice Test<\/a><\/li>\n<li><a href=\"#Geometric_Shapes_and_Angles_Cumulative_Practice\">Geometric Shapes and Angles Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Geometric_Shapes_and_Angles_STEAM_Video\/Performance_Task\"><\/a>Geometric Shapes and Angles STEAM Video\/Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>Track and Field<br \/>\nDifferent lanes on a race track have different lengths. How can competitors run in different lanes and have the same finish line?<\/p>\n<p>Watch the STEAM Video \u201cTrack and Field.\u201d Then answer the following questions.<br \/>\n1. A track consists of a rectangle and two semicircles. The dimensions of the rectangle formed by the innermost lane are shown. What is the distance around each semicircle on the 400-meter, innermost lane?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 1\" width=\"539\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-1.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-1-300x95.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><br \/>\n2. How does the width of the rectangle, 63.7 meters, compare to the distance around each semicircle? Explain.<\/p>\n<p>Answer:<br \/>\n1. The distance around each semicircle on the 400-meter, innermost lane = 488 m<br \/>\n2. The distance around each semicircle = 90\u03c0 + 320<\/p>\n<p>Explanation:<br \/>\n1. The inside perimeter of the track = 400 m<br \/>\nthe total length of the two straight portions = 90 + 90 = 180<br \/>\ntherefore the length of the remaining portion = 400-180 = 220 m<br \/>\ncircumference of the two remaining semi-circular portions = \u03c0r + \u03c0r = 2\u03c0r<br \/>\n2\u03c0r = 220<br \/>\n2 x 3.14 x r = 220<br \/>\nr = 35 m<br \/>\nArea of the track = 2 x 90 x 14 +3.14 x (49) x (49) &#8211; (35) x (35)<br \/>\narea of the track = 6216 square meter<br \/>\nlength of the outer running track = 488 m<br \/>\n2. The perimeter of the track is the two circumferences of the circumferences.<br \/>\nThe diameters of the circle and the width of the rectangle = 90 m<br \/>\n90 \u03c0 + 320<br \/>\n<strong>Performance Task.<br \/>\n<\/strong>Finding the Area and Perimeter of a Track<br \/>\nAfter completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given the dimensions of a race track.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 2\" width=\"575\" height=\"333\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-2.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-2-300x174.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><br \/>\nYou will be asked to solve various perimeter and area problems about the track. Given a race track, what measures do you need to find the outer perimeter?<\/p>\n<p>Answer:<br \/>\nThe outer perimeter = 11,2610 sq m<\/p>\n<p>Explanation:<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) r<br \/>\np = (3.14 + 2)36.5<br \/>\np= (3.16) 36.5<br \/>\np = 11,2610 sq m<\/p>\n<h3><a id=\"Geometric_Shapes_and_Angles_Getting_Ready_for_Chapter_9\"><\/a>Geometric Shapes and Angles Getting Ready for Chapter 9<\/h3>\n<p><strong>Chapter Exploration<\/strong><br \/>\nWork with a partner.<br \/>\nQuestion 1.<br \/>\nPerform the steps for each of the figures.<\/p>\n<ul>\n<li>Measure the perimeter of the larger polygon to the nearest millimeter.<\/li>\n<li>Measure the diameter of the circle to the nearest millimeter.<\/li>\n<li>Measure the perimeter of the smaller polygon to the nearest millimeter.<\/li>\n<li>Calculate the value of the ratio of the two perimeters to the diameter.<\/li>\n<li>Take the average of the ratios. This average is the approximation of \u03c0(the Greek letter ).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 3\" width=\"579\" height=\"343\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-3.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-3-300x178.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/li>\n<\/ul>\n<p>Question 2.<br \/>\nBased on the table, what can you conclude about the value of \u03c0? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nThe value of \u03c0 = 3.14<\/p>\n<p>Explanation:<br \/>\nWe can consider 3 values for the \u03c0.<br \/>\nthey are (22\/7) or 3.14<br \/>\nso i am considering the 3.14<\/p>\n<p>Question 3.<br \/>\nThe Greek mathematician Archimedes used the above procedure to approximate the value of \u03c0. He used polygons with 96 sides. Do you think his approximation was more or less accurate than yours? Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe greek mathematician used polygons with the side of polygons as 12,14,48, and finally 96 sides.<\/p>\n<p>Explanation:<br \/>\nThe greek mathematician used polygons with the side of polygons as 12,14,48, and finally 96 sides.<br \/>\nyes the accuration is more than i think.<\/p>\n<p><strong>Vocabulary<\/strong><br \/>\nThe following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.<br \/>\ndiameter of a circle<br \/>\nsemi circle<br \/>\nadjacent angles<br \/>\ncircumference<br \/>\ncomposite figure<br \/>\nvertical angles<\/p>\n<p>Answer:<br \/>\nThe diameter of the circle = the diameter is the length of the line through the center that touches two points on the edge of the circle.<br \/>\nsemi circle =\u00a0 semicircle is a one-dimensional locus of points that forms half of the circle.<br \/>\nadjacent angles = adjacent angles are two angles that have a common vertex and a common side but do not overlap.<br \/>\ncircumference = the circumference is the perimeter of the circle. the circumference would be the arc length of the circle.<br \/>\ncomposite figure = a figure that consists of two or more geometric shapes.<br \/>\nvertical angles = a pair of non-adjacent angles form when two lines intersect.<\/p>\n<p>Explanation:<br \/>\nThe diameter of the circle = the diameter is the length of the line through the center that touches two points on the edge of the circle.<br \/>\nsemi circle =\u00a0 semicircle is a one-dimensional locus of points that forms half of the circle.<br \/>\nadjacent angles = adjacent angles are two angles that have a common vertex and a common side but do not overlap.<br \/>\ncircumference = the circumference is the perimeter of the circle. the circumference would be the arc length of the circle.<br \/>\ncomposite figure = a figure that consists of two or more geometric shapes.<br \/>\nvertical angles = a pair of non-adjacent angles form when two lines intersect.<\/p>\n<h3><a id=\"Lesson_9.1_Circles_and_Circumference\"><\/a>Lesson 9.1 Circles and Circumference<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using a Compass to Draw a Circle<br \/>\nWork with a partner. Set a compass to 2 inches and draw a circle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 1\" width=\"109\" height=\"223\" \/><br \/>\na. Draw a line from one side of the circle to the other that passes through the center. What is the length of the line? This is called the diameter of the circle.<br \/>\nb. Estimate the distance around the circle. This is called the circumference of the circle. Explain how you found your answer.<\/p>\n<p>Answer:<br \/>\na. the length of the line = 4 inches<br \/>\nb.\u00a0 The circumference of the circle = 12.56 inch<\/p>\n<p>Explanation:<br \/>\na. In the question they said that 2 inches<br \/>\nthe length of the line = 4 in<br \/>\nb. the circumference of the circle = 2\u03c0 r<br \/>\ncircle = 2 x 3.14 x 2<br \/>\ncircle = 12.56 in<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Exploring Diameter and Circumference<br \/>\nWork with a partner.<br \/>\na. Roll a cylindrical object on a flat surface to find the circumference of the circular base.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 2\" width=\"389\" height=\"273\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-2.png 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-2-300x211.png 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><br \/>\nb. Measure the diameter of the circular base. Which is greater, the diameter or the circumference? how many times greater?<br \/>\nc. Compare your answers in part(b) with the rest of the class. What do you notice?<br \/>\nd. Without measuring, how can you find the circumference of a circle with a given diameter? Use your method to estimate the circumference of the circle in Exploration 1.<\/p>\n<p>Answer:<br \/>\na. The circumference of the circle = 2\u03c0r<br \/>\nb. The circumference of the circle is 3.14 times greater than the diameter of the circle.<br \/>\nc. The circumference of the circle is greater than the diameter of the circle.<br \/>\nd. The diameter of the circle = 2r and the circumference of the circle = 2\u03c0r<\/p>\n<p>Explanation:<br \/>\na. The circumference of the circle = 2\u03c0r<br \/>\nb. The circumference of the circle is 3.14 times greater than the diameter of the circle.<br \/>\nc. The circumference of the circle is greater than the diameter of the circle.<br \/>\nd. The diameter of the circle = 2r and the circumference of the circle = 2\u03c0r<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-27856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 3\" width=\"185\" height=\"171\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nThe diameter of a circle is 16 centimeters. Find the radius.<\/p>\n<p>Answer:<br \/>\nradius = 8 cm<\/p>\n<p>Explanation:<br \/>\nThe diameter of the circle = 2r<br \/>\n16 = 2r<br \/>\nr = 8 cm<\/p>\n<p>Question 2.<br \/>\nThe radius of a circle is 9 yards. Find the diameter.<\/p>\n<p>Answer:<br \/>\nThe diameter = 18 yds<\/p>\n<p>Explanation:<br \/>\nThe diameter of the circle = 2r<br \/>\ndiameter = 2 x 9<br \/>\nr = 18 yds<\/p>\n<p><strong>Find the circumference of the object. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 4\" width=\"125\" height=\"103\" \/><\/p>\n<p>Answer:<br \/>\ncircumference = 12.56 cm<\/p>\n<p>Explanation:<br \/>\ncircumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 2 where r = 2cm given<br \/>\ncircle = 6.28 x 2<br \/>\ncircle = 12.56 cm<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 5\" width=\"126\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\ncircumference =43.96 square feet<\/p>\n<p>Explanation:<br \/>\ncircumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 7 where r = 7 ft given<br \/>\ncircle = 6.28 x 7<br \/>\ncircle = 43.96 square feet<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 6\" width=\"105\" height=\"103\" \/><\/p>\n<p>Answer:<br \/>\ncircumference =28.26 square in<\/p>\n<p>Explanation:<br \/>\ncircumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 4.5 where r = 4.5 is given<br \/>\ncircle = 6.28 x 4.5<br \/>\ncircle =28.26 in<\/p>\n<p><strong>Find the perimeter of the semicircular region.<\/strong><br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 7\" width=\"136\" height=\"85\" \/><\/p>\n<p>Answer:<br \/>\nperimeter of the semicircle =\u00a0 5.14 ft<\/p>\n<p>Explanation:<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) r<br \/>\nperimeter = (3.14 + 2) 1 diameter = 2 given r= 1<br \/>\nperimeter = 5.14 feet<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 8\" width=\"139\" height=\"95\" \/><\/p>\n<p>Answer:<br \/>\nperimeter of the semicircle =\u00a0 17.99 cm<\/p>\n<p>Explanation:<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) r<br \/>\nperimeter = (3.14 + 2) 3.5 diameter = 7 given r= 3.5<br \/>\nperimeter = 17.99 cm<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 9\" width=\"133\" height=\"91\" \/><\/p>\n<p>Answer:<br \/>\nthe perimeter of the semicircle =\u00a0 33.14 in<\/p>\n<p>Explanation:<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) r<br \/>\nperimeter = (3.14 + 2) 15 given r= 15<br \/>\nperimeter = 33.14 in<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\n<strong>WRITING<\/strong><br \/>\nAre there circles for which the value of the ratio of circumference to diameter is not equal to \u03c0? Explain.<\/p>\n<p>Answer:<br \/>\ncircumference to diameter is equal to \u03c0<\/p>\n<p>Explanation:<br \/>\nd. The diameter of the circle = 2r and the circumference of the circle = 2\u03c0r<br \/>\ncircumference to diameter is equal to \u03c0<\/p>\n<p>Question 10.<br \/>\n<strong>FINDING A PERIMETER<\/strong><br \/>\nFind the perimeter of a semicircular region with a straight side that is 8 yards long.<\/p>\n<p>Answer:<br \/>\nperimeter = 11.14 yd<\/p>\n<p>Explanation:<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) r<br \/>\nperimeter = (3.14 + 2) 4 given r= 4<br \/>\nperimeter = 11.14 yd<br \/>\nQuestion 11.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 10\" width=\"559\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-10.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-10-300x67.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Answer:<br \/>\nWhat is \u03c0 times the radius?<br \/>\nWhat is \u03c0 times the diameter?<\/p>\n<p>Explanation:<br \/>\nthe radius of the circle = (c\/2 \u03c0 )<br \/>\nthe diameter of the circle =\u00a0 2r<br \/>\n<strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 12.<br \/>\nThe wheels of a monster truck are 66 inches tall. Find the distance the monster truck travels when the tires make one 360-degree rotation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 11\" width=\"204\" height=\"145\" \/><\/p>\n<p>Answer:<br \/>\nThe distance = 207.35 inches<\/p>\n<p>Explanation:<br \/>\nThe wheel is in the shape of a circle.<br \/>\ndiameter = 66 given<br \/>\nradius = (66\/2)<br \/>\nradius = 33<br \/>\nThe circumference = 2\u03c0r<br \/>\nc = 2 x 3.14 x 33<br \/>\nc = 6.28 x 33<br \/>\nc = 207.24 in<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe radius of a dog\u2019s collar should be at least 0.5 inch larger than the radius of the dog\u2019s neck. A dog collar adjusts to a circumference of 10 to 14 inches. Should the collar be worn by a dog with a neck circumference of 12.5 inches? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 12\" width=\"165\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nNo, the collar should not be worn by this dog.<\/p>\n<p>Explanation:<br \/>\nGiven that the collar should be at least 0.5 inches.<br \/>\ndog collar adjusts to a circumference of 10 to 14 inches.<\/p>\n<p>Question 14.<br \/>\nYou resize a picture so that the radius of the midday Sun appears four times larger. How much larger does the circumference of the Sun appear? Explain.<\/p>\n<p>Answer:<br \/>\n4 times larger<\/p>\n<p>Explanation:<br \/>\nthey said that if they resize it for 4 times.<br \/>\ntherefore the sun appears 4 times larger.<\/p>\n<h3><a id=\"Circles_and_Circumference_Homework_&amp;_Practice_9.1\"><\/a>Circles and Circumference Homework &amp; Practice 9.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Two jars each contain 1000 numbered tiles. The double box-and-whisker plot represents a random sample of 10 numbers from each jar.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 13\" width=\"227\" height=\"106\" \/><br \/>\nQuestion 1.<br \/>\nCompare the samples using measures of center and variation.<\/p>\n<p>Answer:<br \/>\na. Jar A = median 3, starting 2.<br \/>\nb. Jar B = median\u00a0 6, starting 2<\/p>\n<p>Explanation:<br \/>\nIn the above-given figure, the jar A is starting from 2<br \/>\njar A contains median = 3<br \/>\nthe jar B is starting from 2<br \/>\njar B contains median = 6<\/p>\n<p>Question 2.<br \/>\nCan you determine which jar contains greater numbers? Explain.<\/p>\n<p>Answer:<br \/>\nJar B<\/p>\n<p>Explanation:<br \/>\njar B contains the numbers from 4 to 9<br \/>\nQuestion 3.<br \/>\nFind the percent of change from 24 to 18.<br \/>\nA. 25% decrease<br \/>\nB. 25% increase<br \/>\nC. 75% increase<br \/>\nD. 75% decrease<\/p>\n<p>Answer:<br \/>\noption A is correct<\/p>\n<p>Explanation:<br \/>\nif the percent of jar changes from 24 to 18<br \/>\nthe decrease in the percent = 25<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>EXPLORING DIAMETER AND CIRCUMFERENCE<\/strong> Estimate the circumference of the circular base of the object. (See Exploration 2, p. 361.)<br \/>\nQuestion 4.<br \/>\ntube of lip balm with radius 0.5 mm<\/p>\n<p>Answer:<br \/>\nc = 3.14 mm<\/p>\n<p>Explanation:<br \/>\ncircumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 0.5 where r = 0.5 mm given<br \/>\ncircle = 6.28 x 0.5<br \/>\ncircle =3.14 mm<\/p>\n<p>Question 5.<br \/>\nD battery with radius 0.65 in.<\/p>\n<p>Answer:<br \/>\nc = 4.082 in<\/p>\n<p>Explanation:<br \/>\ncircumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 0.65 where r = 0.65 ingiven<br \/>\ncircle = 6.28 x 0.65<br \/>\ncircle =4.082 in<\/p>\n<p><strong>FINDING A RADIUS<\/strong> Find the radius of the button.<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 14\" width=\"144\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nradius =2.5 cm<\/p>\n<p>Explanation:<br \/>\nradius = (5\/2)<br \/>\nradius = 2.5 cm<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 15\" width=\"159\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nradius =14 mm<\/p>\n<p>Explanation:<br \/>\nradius = (28\/2)<br \/>\nradius = 14 mm<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 16\" width=\"144\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nradius =1.75 in<\/p>\n<p>Explanation:<br \/>\nradius = (3.5\/2)<br \/>\nradius = 1.75 in<\/p>\n<p><strong>FINDING A DIAMETER<\/strong> Find the diameter of the object.<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 17\" width=\"122\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\ndiameter = 4 in<\/p>\n<p>Explanation:<br \/>\ndiameter of the circle = 2r<br \/>\nwhere r = 2 given<br \/>\nd = 4 in<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 18\" width=\"135\" height=\"135\" \/><\/p>\n<p>Answer:<br \/>\ndiameter = 0.64 ft<\/p>\n<p>Explanation:<br \/>\ndiameter of the circle = 2r<br \/>\nwhere r = 0.8 given<br \/>\nd = 0.64 ft<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 19\" width=\"138\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\ndiameter = 1.2 cm<\/p>\n<p>Explanation:<br \/>\ndiameter of the circle = 2r<br \/>\nwhere r = 0.6 given<br \/>\nd = 1.2 cm<\/p>\n<p><strong>FINDING A CIRCUMFERENCE<\/strong> Find the circumference of the object. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<br \/>\nQuestion 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-20.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 20\" width=\"141\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nc = 43.96 in<\/p>\n<p>Explanation:<br \/>\ncircumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 7 where r = 7 ingiven<br \/>\ncircle = 6.28 x 7<br \/>\ncircle =43.96 in<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-21.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 21\" width=\"143\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nc = 18.84 cm<\/p>\n<p>Explanation:<br \/>\ncircumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 7 where r = 3 cmgiven<br \/>\ncircle = 6.28 x 3<br \/>\ncircle =18.84 cm<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-22.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 22\" width=\"166\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nc = 6.28 mm<\/p>\n<p>Explanation:<br \/>\ncircumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 1where r = 1mgiven<br \/>\ncircle = 6.28 x 1<br \/>\ncircle =6.28 m<\/p>\n<p><strong>FINDING THE PERIMETER OF A SEMICIRCULAR REGION<\/strong> Find the perimeter of the window.<br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-23.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 23\" width=\"211\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nperimeter = 7.71 ft<\/p>\n<p>Explanation:<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) r<br \/>\nperimeter = (3.14 + 2) 1.5 given d =3 ,r = (d\/2)<br \/>\nperimeter = 7.71 ft<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-24.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 24\" width=\"213\" height=\"127\" \/><\/p>\n<p>Answer:<br \/>\nperimeter = 64.8 cm<\/p>\n<p>Explanation:<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) r<br \/>\nperimeter = (3.14 + 2) 20 given\u00a0 ,r = 20 cm<br \/>\nperimeter = 64.8 cm<\/p>\n<p><strong>ESTIMATING A RADIUS<\/strong> Estimate the radius of the object.<br \/>\nQuestion 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-25.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 25\" width=\"131\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nRadius = 1.417 mm<\/p>\n<p>Explanation:<br \/>\nradius of the circle =\u00a0(c\/2\u03c0 )<br \/>\nr = (8.9\/6.28)<br \/>\nr = 1.417 mm<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-26.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 26\" width=\"160\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nRadius = 19.426 in<\/p>\n<p>Explanation:<br \/>\nradius of the circle =\u00a0(c\/2\u03c0 )<br \/>\nr = (122\/6.28)<br \/>\nr = 19.426 in<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA circular sinkhole has a circumference of 75.36 meters. A week later, it has a circumference of 150.42 meters.<br \/>\na. Estimate the diameter of the sinkhole each week.<br \/>\nb. How many times greater is the diameter of the sinkhole a week later?<\/p>\n<p>Answer:<br \/>\na. The diameter of the sinkhole each week = 4 in<br \/>\nb. 2 times greater is the diameter of the sinkhole a week later<\/p>\n<p>Explanation:<br \/>\na. The diameter of the sinkhole each week = 75.36 m<br \/>\nb. 2 times greater is the diameter of the sinkhole a week later<br \/>\n75.36 x 75.36 = 150.42 m<br \/>\nQuestion 20.<br \/>\n<strong>REASONING<\/strong><br \/>\nConsider the circles A, B, C, and D.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-27.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 27\" width=\"507\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-27.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-27-300x66.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><br \/>\na. Without calculating, which circle has the greatest circumference? Explain.<br \/>\nb. Without calculating, which circle has the least circumference? Explain.<\/p>\n<p>Answer:<br \/>\na. option D has the greatest circumference.<br \/>\nb. option C has the least circumference.<\/p>\n<p>Explanation:<br \/>\nD. circumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 50where r =50 ingiven<br \/>\ncircle = 6.28 x 50<br \/>\ncircle =314 in<br \/>\nExplanation:<br \/>\nC. circumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 1where r = 1given<br \/>\ncircle = 6.28 x1<br \/>\ncircle = 6.28<br \/>\nExplanation:<br \/>\nA. circumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 4 where r = 4given<br \/>\ncircle = 6.28 x 4<br \/>\ncircle = 25.12<br \/>\nExplanation:<br \/>\nA. circumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 10 where r = 10given<br \/>\ncircle = 6.28 x 10<br \/>\ncircle = 62.8<\/p>\n<p><strong>FINDING CIRCUMFERENCES<\/strong> Find the circumferences of both circles.<br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-28.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 28\" width=\"134\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\ncircumference of inside circle\u00a0 =31.4 square cm<br \/>\ncircumference of outside circle = 62.8\u00a0 square cm<\/p>\n<p>Explanation:<br \/>\ncircumference of the inside circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 5 where r = 5 cm given<br \/>\ncircle = 6.28 x 5<br \/>\ncircle = 31.4 square cm<br \/>\ncircumference of the outside circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 2 where r = 2 cm given<br \/>\ncircle = 6.28 x 2<br \/>\ncircle = 62.8 square cm<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-29.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 29\" width=\"131\" height=\"114\" \/><\/p>\n<p>Answer:<br \/>\ncircumference of inside circle\u00a0 =28.26 ft<br \/>\ncircumference of outside circle = 31.4 square cm<\/p>\n<p>Explanation:<br \/>\ncircumference of the inside circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 4.5 where r = 4.5 feet given<br \/>\ncircle = 6.28 x 4.5<br \/>\ncircle = 28.26 ft<br \/>\ncircumference of the outsideside circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 2.5 where r = 2.5 ft given<br \/>\ncircle = 6.28 x 2.5<br \/>\ncircle = 15.7 square ft<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-30.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 30\" width=\"114\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\ncircumference of inside circle\u00a0 =69.08\u00a0 m<br \/>\ncircumference of outside circle = 138.16 m<\/p>\n<p>Explanation:<br \/>\ncircumference of the inside circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 5.5 where r = 5.5 feet given<br \/>\ncircle = 6.28 x 5.5<br \/>\ncircle = 69.08 m<br \/>\ncircumference of the outsideside circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 22 where r = 22given<br \/>\ncircle = 6.28 x 22<br \/>\ncircle = 138.16 m<\/p>\n<p>Question 24.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA satellite is in an approximately circular orbit 36,000 kilometers from Earth\u2019s surface. The radius of Earth is about 6400 kilometers. What is the circumference of the satellite\u2019s orbit?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-31.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 31\" width=\"187\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\nc = 40,192 km<\/p>\n<p>Explanation:<br \/>\ncircumference of the\u00a0 satellite orbit =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 6400where r = 6400kmgiven<br \/>\ncircle = 6.28 x 6400<br \/>\ncircle =40,192km<\/p>\n<p>Question 25.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nThe ratio of circumference to diameter is the same for every circle. Is the ratio of circumference to radius the same for every circle? Explain.<\/p>\n<p>Answer:<br \/>\nThe ratio of circumference to radius is\u00a0 same for every circle.<\/p>\n<p>Explanation:<br \/>\nc\/r = 2\u03c0r\/r<br \/>\nwhere r get canceled in both numerator and denominator.<br \/>\nc\/r = 2\u03c0<br \/>\nradius = (c\/2\u03c0)<br \/>\nthe radius is same for every circle.<\/p>\n<p>Question 26.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA wire is bent to form four semicircles. How long is the wire? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-32.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 32\" width=\"299\" height=\"84\" \/><\/p>\n<p>Answer:<br \/>\nThe wire is 128 cm long<\/p>\n<p>Explanation:<br \/>\nGiven that the four semicircles are 32 cm<br \/>\n32 + 32 + 32 + 32 = 64<\/p>\n<p>Question 27.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nExplain how to draw a circle with a circumference of \u03c0<sup>2<\/sup> inches. Then draw the circle.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-12.png\" alt=\"\" width=\"226\" height=\"230\" \/><\/p>\n<p>Explanation:<br \/>\ncircumference of circle = 2\u03c0r<br \/>\nc = \u03c0<sup>2<\/sup><\/p>\n<p>Question 28.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\n\u201cLines\u201d of latitude on Earth are actually circles. The Tropic of Cancer is the northernmost line of latitude at which the Sun appears directly overhead at noon. The Tropic of Cancer has a radius of 5854 kilometers.<br \/>\nTo qualify for an around-the-world speed record, a pilot must cover a distance no less than the circumference of the Tropic of Cancer, cross all meridians, and land on the same air \ufb01eld where the flight began.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-33.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 33\" width=\"239\" height=\"222\" \/><br \/>\na. What is the minimum distance that a pilot must \ufb02y to qualify for an around-the-world speed record?<br \/>\nb. RESEARCH Estimate the time it will take for a pilot to qualify for the speed record. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. The minimum distance that a pilot must fly to qualify for an around the world-speed record = 18.3376 km<br \/>\nb. The pilot will take for the speed record = 18.3376 km<\/p>\n<p>Explanation:<br \/>\na. The minimum distance that a pilot must fly to qualify for an around the world-speed record = 18.3376 km<br \/>\nb. The pilot will take for the speed record = 18.3376 km<br \/>\nQuestion 29.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nBicycles in the late 1800s looked very different than they do today.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-34.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 34\" width=\"164\" height=\"142\" \/><br \/>\na. How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number.<br \/>\nb. Would you rather ride a bicycle made with two large wheels or two small wheels? Explain.<\/p>\n<p>Answer:<br \/>\na. The rotations each tire make after traveling 600 feet = 188.4 in in<br \/>\nb. two large wheels = 376.8 in<br \/>\ntwo small wheels = 113.04 in<\/p>\n<p>Explanation:<br \/>\nthe rotations each tire make after travelling = 2 x 3.14 x 30\u00a0 = 188.4 in<br \/>\nb. two large wheels = 188.4 x 2 = 376.8 in<br \/>\nfor two small wheels = 113.04 in<\/p>\n<p>Question 30.<br \/>\n<strong>LOGIC<\/strong><br \/>\nThe length of the minute hand is 150% of the length of the hour hand.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.1-35.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.1 35\" width=\"181\" height=\"250\" \/><br \/>\na. What distance will the tip of the minute hand move in 45 minutes? Justify your answer.<br \/>\nb. In 1 hour, how much farther does the tip of the minute hand move than the tip of the hour hand? Explain how you found your answer.<\/p>\n<p>Answer:<br \/>\nThe distance will the tip of minute hand move in 45 minutes = 140 %<br \/>\nb. the tip of the minute hand moves 60 times faster than hour hand.<\/p>\n<p>Explanation:<br \/>\nThe distance will the tip of minute hand move in 45 minutes = 140 %<br \/>\nb. the tip of the minute hand moves 60 times faster than hour hand.<\/p>\n<h3><a id=\"Lesson_9.2_Areas_of_Circles\"><\/a>Lesson 9.2 Areas of Circles<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Estimating the Area of a Circle<br \/>\nWork with a partner. Each grid contains a circle with a diameter of 4 centimeters. Use each grid to estimate the area of the circle. Which estimate should be closest to the actual area? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 1\" width=\"502\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-1.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-1-300x100.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Answer:<br \/>\nArea of 1st circle = 200.96 cm<br \/>\nArea of 2nd circle =803.84 cm<br \/>\nArea of 3rd circle =3215.36 cm<\/p>\n<p>Explanation:<br \/>\narea of 1st circle = \u03c0r x r<br \/>\narea = 3.14 x 8 x 8<br \/>\na = 200.96 cm<br \/>\n<span style=\"font-size: 16px; font-style: normal; font-weight: 400;\">area of 2nd circle = \u03c0r x r<br \/>\n<\/span><span style=\"font-size: 16px; font-style: normal; font-weight: 400;\">area<\/span>= 3.14 x 16 x 16<br \/>\na = 803.84 cm<br \/>\n<span style=\"font-size: 16px; font-style: normal; font-weight: 400;\">area of 3rd circle = \u03c0r x r<br \/>\n<\/span><span style=\"font-size: 16px; font-style: normal; font-weight: 400;\">area<\/span>= 3.14 x 32 x 32<br \/>\na = 3215.36<br \/>\n<strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing a Formula for the Area of a Circle<br \/>\nWork with a partner. A student draws a circle with radius and divides the circle into 24 equal sections. The student cuts out each section and arranges the sections to form a shape that resembles a parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-2.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 2\" width=\"634\" height=\"183\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-2.png 634w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-2-300x87.png 300w\" sizes=\"(max-width: 634px) 100vw, 634px\" \/><br \/>\na. Use the diagram to write a formula for the area of a circle in terms of the radius r. Explain your reasoning.Describe the relationship between the radius and the area of a circle.<br \/>\nb. Use the formula to check your estimates in Exploration 1.<\/p>\n<p>Answer:<br \/>\na. the area of the circle = 1808.64<br \/>\nb. the area of the circle in terms of radius r = 0.0084 cm<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 24 x 24<br \/>\na = 1808.64 cm<br \/>\nThe radius of the circle = (c\/2 \u03c0)<br \/>\ncircumference = 2\u03c0r<br \/>\nc = 2 x 3.14 x 24<br \/>\nc = 150.72 cm<br \/>\narea = (150.72\/6.28)<br \/>\narea = 0.0084 cm<\/p>\n<p><strong>Try It<br \/>\n<\/strong>Question 1.<br \/>\nFind the area of a circle with a radius of 6 feet. Use 3.14 for \u03c0.<\/p>\n<p>Answer:<br \/>\nThe area\u00a0 of circle = 113.04 sq ft<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 6 x 6<br \/>\na = 113.04 square feet<br \/>\nQuestion 2.<br \/>\nFind the area of a circle with a diameter of 28 meters.Use \\(\\frac{22}{7}\\) for \u03c0.<\/p>\n<p>Answer:<br \/>\nThe area\u00a0 of circle = 175.84 sq meters<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 14 x 14 where d = 28 so r = 14<br \/>\na = 175.84 square meters<\/p>\n<p><strong>Find the area of the semicircle.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-3.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 3\" width=\"112\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\nArea of semicircle =62.07 sq cm<\/p>\n<p>Explamation:<br \/>\nArea of semicircle =( \u03c0+r x r\/2)<br \/>\narea =( 3.14 +121\/2)<br \/>\narea =(121.14\/2)<br \/>\narea = 62.07 sq cm<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-4.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 4\" width=\"143\" height=\"93\" \/><\/p>\n<p>Answer:<br \/>\nArea of semicircle =9.57 sqm<\/p>\n<p>Explamation:<br \/>\nArea of semicircle =( \u03c0+r x r\/2)<br \/>\narea =( 3.14 +16\/2)<br \/>\narea =(19.14\/2)<br \/>\narea = 9.57 sq m<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-5.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 5\" width=\"139\" height=\"103\" \/><\/p>\n<p>Answer:<br \/>\nArea of semicircle =4.695 sq yd<\/p>\n<p>Explanation:<br \/>\nArea of semicircle =( \u03c0+r x r\/2)<br \/>\narea =( 3.14 +6.25\/2)<br \/>\narea =(9.39\/2)<br \/>\narea = 4.695 sq yd<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 6.<br \/>\n<strong>ESTIMATING AN AREA<\/strong><br \/>\nThe grid contains a circle with a diameter of 2 centimeters. Use the grid to estimate the area of the circle. How can you change the grid to improve your estimate? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-6.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 6\" width=\"93\" height=\"93\" \/><\/p>\n<p>Answer:<br \/>\nThe area\u00a0 of circle = 50.24 sq centi meters<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 4 x 4 where d = 8 so r = 4<br \/>\na = 50.24 square centimeters<\/p>\n<p>Question 7.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain the relationship between the circumference and area of a circle.<\/p>\n<p>Answer:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\ncircumference of circle = 2\u03c0r<\/p>\n<p>Explanation:<br \/>\nThe circumference of the circle is 2 times greater than the area of the circle.<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\ncircumference of circle = 2\u03c0r<\/p>\n<p>Question 8.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-7.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 7\" width=\"419\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-7.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-7-300x90.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<p>Answer:<br \/>\nWhat is area of a circle with a radius of 100 cm?<br \/>\nWhat is the area of a circle with a radius\u00a0 of 500 mm?<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\narea = 3.14 x 100 x 100<br \/>\narea = 31400 sq cm<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\narea = 3.14 x 500 x 500<br \/>\narea = 785000 sq mm<br \/>\n<strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\nA local event planner wants to cover a circular region with mud for an obstacle course. The region has a circumference of about 157 feet. The cost to cover 1 square foot with mud is $1.50. Approximate the cost to cover the region with mud.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-8.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 8\" width=\"188\" height=\"135\" \/><\/p>\n<p>Answer:<br \/>\nCost to cover =<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA manufacturer recommends that you use a frying pan with a radius that is within 1 inch of the radius of your stove top burner. The area of the bottom of your frying pan is 25\u03c0 square inches. The circumference of your cook top burner is 9\u03c0 inches. Does your frying pan meet the manufacturer\u2019s recommendation?<\/p>\n<p>Answer:<br \/>\nno the frying pan does not meet the manufacture<\/p>\n<p>Explanation:<br \/>\nGiven that frying pan has radius = 1 inch<br \/>\narea of frying pan = 25\u03c0 square inches<br \/>\ncircumference = 9\u03c0\u00a0 inches<\/p>\n<h3><a id=\"Areas_of_Circles_Homework_&amp;_Practice_9.2\"><\/a>Areas of Circles Homework &amp; Practice 9.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the circumference of the object. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-9.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 9\" width=\"154\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nc = 28.26cm<\/p>\n<p>Explanation:<br \/>\ncircumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 4.5where r = 4.5cmgiven<br \/>\ncircle = 6.28 x 4.5<br \/>\ncircle =28.26 cm<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-10.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 10\" width=\"144\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\nc = 21.98 sq in<\/p>\n<p>Explanation:<br \/>\ncircumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 3.5where r = 3.5ingiven<br \/>\ncircle = 6.28 x 3.5<br \/>\ncircle =21.98 sq in<\/p>\n<p><strong>You spin the spinner shown.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-11.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 11\" width=\"98\" height=\"89\" \/><br \/>\nQuestion 3.<br \/>\nHow many possible outcomes are there?<\/p>\n<p>Answer:<br \/>\n3 possible outcomes<\/p>\n<p>Explanation:<br \/>\nThere are 3 possible outcomes.<br \/>\n3 numbers are there in the spin.<\/p>\n<p>Question 4.<br \/>\nIn how many ways can spinning an odd number occur?<\/p>\n<p>Answer:<br \/>\n2 ways the spinning an odd number occur.<\/p>\n<p>Explanation:<br \/>\nThere are 2 possible ways that the odd numbers can occur.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>ESTIMATING AN AREA<\/strong> Use the grid to estimate the area of the circle. (See Exploration 1, p. 369.)<\/p>\n<p>Question 5.<br \/>\ndiameter of 3 centimeters<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-12.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 12\" width=\"138\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\narea of the circle = 6.75 sq cm<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\narea = 3.14 x 1.5 x 1.5<br \/>\narea = 6.75 sq cm<\/p>\n<p>Question 6.<br \/>\ndiameter of 1.6 inches<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-13.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 13\" width=\"167\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-13.png 167w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-13-150x150.png 150w\" sizes=\"(max-width: 167px) 100vw, 167px\" \/><\/p>\n<p>Answer:<br \/>\narea of the circle = 141.41 sq in<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\narea = 3.14 x 6.4 x 6.4<br \/>\narea = 141.41 sq in<\/p>\n<p><strong>FINDING AN AREA<\/strong> Find the area of the circle. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-14.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 14\" width=\"170\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\nThe area\u00a0 of circle = 254.34 sq milli meters<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 4 x 4 where d = 8 so r = 4<br \/>\na = 254.34 square millimeters<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-15.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 15\" width=\"170\" height=\"135\" \/><\/p>\n<p>Answer:<br \/>\nThe area\u00a0 of circle = 615.44 sq centi meters<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 14 x 14 where r = 14<br \/>\na = 615.44 square centimeters<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-16.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 16\" width=\"170\" height=\"131\" \/><\/p>\n<p>Answer:<br \/>\nThe area\u00a0 of circle = 314 sq inches<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 10 x 10 where r = 10<br \/>\na = 314 square inches<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-17.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 17\" width=\"160\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nThe area\u00a0 of circle = 7.065 sq inches<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 1.5 x 1.5 where r = 1.5<br \/>\na = 7.065 square inches<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-18.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 18\" width=\"162\" height=\"137\" \/><\/p>\n<p>Answer:<br \/>\nThe area\u00a0 of circle = 3.14 sq cm<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 1 x 1 where r = 1<br \/>\na = 3.14 square cm<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-19.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 19\" width=\"199\" height=\"131\" \/><\/p>\n<p>Answer:<br \/>\narea\u00a0 of circle = 1.76625sq ft<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 0.75 x 0.75 where r = 0.75<br \/>\na = 1.76625 square ft<\/p>\n<p>Question 13.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the area of a circle with a diameter of 7 meters. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-20.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 20\" width=\"241\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nNo, my friend is not correct.<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of circle = \u03c0r x r<br \/>\na = 3.14 x 3.5 x 3.5 where r = 0.75<br \/>\na = 38.465 square meters<br \/>\nQuestion 14.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe diameter of a flour tortilla is 12 inches. What is the total area of two tortillas?<\/p>\n<p>Answer:<br \/>\nThe area\u00a0 of tortilla = 226.08 sq inches<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of tortilla = \u03c0r x r<br \/>\na = 3.14 x 6 x 6 where r = 6<br \/>\na = 113.04 square inches<br \/>\nfor 2 tortilla = 226.08 sq inches<\/p>\n<p>Question 15.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe diameter of a coaster is 7 centimeters. What is the total area of five coasters?<\/p>\n<p>Answer:<br \/>\nThe\u00a0 total area\u00a0 of coaster = 192.325 cm<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of tortilla = \u03c0r x r<br \/>\na = 3.14 x 3.5 x 3.5 where r = 3.5<br \/>\na = 38.465 square cm<br \/>\nfor 5 tortilla = 192.325 centimeters<\/p>\n<p>Question 16.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe HillsboroInlet Lighthouse lights up how much more area than the Jupiter Inlet Lighthouse?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-21.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 21\" width=\"181\" height=\"204\" \/><\/p>\n<p>Answer:<br \/>\nThe HillsboroInlet Lighthouse lights are 2 times greater than the Jupiter Inlet Lighthouse.<\/p>\n<p>Explanation:<br \/>\nHillsboro inlet Lighthouse = 3.14 x 28 x 28<br \/>\narea = 2,461.76 sq mi<br \/>\njupiter inlet Lighthouse = 3.14 x 18 x 18<br \/>\narea = 1,017.36 sq mi<\/p>\n<p><strong>FINDING THE AREA OF A SEMICIRCLE<\/strong> Find the area of the semicircle.<br \/>\nQuestion 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-22.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 22\" width=\"188\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nArea of semicircle = 628 sq cm<\/p>\n<p>Explanation:<br \/>\nArea of semicircle =( \u03c0+r x r\/2)<br \/>\narea =( 3.14 +400\/2)<br \/>\narea =(403.14\/2)<br \/>\narea = 628 sq cm<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-23.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 23\" width=\"186\" height=\"120\" \/><br \/>\nAnswer:<br \/>\nArea of semicircle =201.57 sq cm<\/p>\n<p>Explanation:<br \/>\nArea of semicircle =( \u03c0+r x r\/2)<br \/>\narea =( 3.14 +400\/2)<br \/>\narea =(403.14\/2)<br \/>\narea = 201.57 sq cm<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-24.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 24\" width=\"192\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nArea of semicircle =1.57 sq ft<\/p>\n<p>Explanation:<br \/>\nArea of semicircle =( \u03c0+r x r\/2)<br \/>\narea =( 3.14 +1\/2)<br \/>\narea =(3.14\/2)<br \/>\narea = 1.57 sq ft<\/p>\n<p>Question 20.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe plate for a microscope has a circumference of 100\u03c0 millimeters. What is the area of the plate?<\/p>\n<p>Answer:<br \/>\nArea of the plate = 200\u03c0 mm<\/p>\n<p>Explanation:<br \/>\nArea of the plate = \u03c0 x r x r<br \/>\narea = 3.14 x 200 x 200<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA dog is leashed to the corner of a house. How much running area does the dog have? Explain how you found your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-25.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 25\" width=\"144\" height=\"161\" \/><\/p>\n<p>Answer:<br \/>\nArea of the circle = 942 sq ft<\/p>\n<p>Explanation:<br \/>\nArea of the circle = \u03c0 x r x r<br \/>\narea = 3.14 x 20 x 20<br \/>\narea = 942 sq ft<br \/>\nThe running area is 3\/4 the area of a circle with a radius of 20 feet.<\/p>\n<p>Question 22.<br \/>\n<strong>REASONING<\/strong><br \/>\nTarget A has a circumference of 20 feet. Target B has a diameter of 3 feet. Both targets are the same distance away. Which target is easier to hit? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nTarget B is easier to hit<\/p>\n<p>Explanation:<br \/>\nTarget A =2\u00a0 \u03c0 x r<br \/>\nA\u00a0 = 2 x 3.14 x 3.18<br \/>\nA = 19.9704<\/p>\n<p>Target B = 1.5<\/p>\n<p>Question 23.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA circular oil spill has a radius of 2 miles. After a day, the radius of the oil spill increases by 3 miles. By how many square miles does the area of the oil spill increase?<\/p>\n<p>Answer:<br \/>\nThe area of oil spill increases by 65.94 miles.<\/p>\n<p>Explanation:<br \/>\nGiven that the circular oil spill has a radius of 2 miles.<br \/>\nThe radius of the oil spill increases by 65.94 sq miles.<\/p>\n<p>Question 24.<br \/>\n<strong>FINDING AN AREA<\/strong><br \/>\nFind the area of the circle in square yards.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-9.2-26.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles 9.2 26\" width=\"108\" height=\"104\" \/><\/p>\n<p>Answer:<br \/>\nArea of the circle = 7.057935 sq yd<\/p>\n<p>Explanation:<br \/>\nArea of the circle = \u03c0 x r x r<br \/>\narea = 3.14 x 4.5 x 4.5<br \/>\narea = 63.585 sq ft<br \/>\narea = 7.057935 sq yd<\/p>\n<p>Question 25.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nWhat happens to the circumference and the area of a circle when you double the radius? triple the radius? Justify your answer.<\/p>\n<p>Answer:<br \/>\nIf we double the radius ,area\u00a0 = \u03c0 x r x r x r x r<br \/>\nIf we double the radius, circumference\u00a0 = 2\u03c0r x r x r<br \/>\nIf we triple the radius ,area\u00a0 = \u03c0 x r x r x r x r x r<br \/>\nIf we triple the radius, circumference\u00a0 = 2\u03c0r x r x r x r x r<\/p>\n<p>Explanation:<br \/>\ncircumference doubles and area quadruples;<br \/>\ncircumference triples and area is 9 times greater;<br \/>\ndouble the radius: circumference = 2\u03c02r = 4\u03c0r<br \/>\n4\u03c0r \/2\u03c0r\u00a0 = 2 times larger, area =\u03c0 (2r) x r =4\u03c0rx r<br \/>\n4\u03c0rx r\/ \u03c0rx r = 4 times larger.<\/p>\n<p>Question 26.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs the area of a semicircle with a diameter of x greater than, less than, or equal to the area of a circle with a diameter of \\(\\frac{1}{2}\\)x? Explain.<\/p>\n<p>Answer:<br \/>\nThe area of a semicircle with a diameter of x is greater than the area of a circle with a diameter of (0.5)<\/p>\n<p>Explanation:<br \/>\nArea of semicircle = (3.14 + (0.5 x 0.5)\/2)<br \/>\narea = 1.695<br \/>\nArea of circle = (3.14 x 0.5 x 0.5)<br \/>\narea = 0.785<\/p>\n<h3><a id=\"Lesson_9.3_Perimeters_and_Areas_of_Composite_Figures\"><\/a>Lesson 9.3 Perimeters and Areas of Composite Figures<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Submitting a Bid<br \/>\nWork with a partner. You want to bid on a project for the pool shown. The project involves ordering and installing the brown tile that borders the pool, and ordering a custom-made tarp to cover the surface of the pool. In the \ufb01gure, each grid square represents 1 square foot. You pay $5 per linear foot for the tile.<\/p>\n<ul>\n<li>You pay $4 per square foot for the tarp.<\/li>\n<li>It takes you about 15 minutes to install each foot of tile.<\/li>\n<\/ul>\n<p>a. Estimate the total cost for the tile and the tarp.<br \/>\nb. Write a bid for how much you will charge for the project.Include the hourly wage you will receive.Estimate your total profit.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 1\" width=\"629\" height=\"477\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-1.png 629w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-1-300x228.png 300w\" sizes=\"(max-width: 629px) 100vw, 629px\" \/><\/p>\n<p>Answer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-27916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 2\" width=\"188\" height=\"86\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nEstimate the perimeter and the area of the figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-3.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 3\" width=\"171\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-3.png 171w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-3-150x150.png 150w\" sizes=\"(max-width: 171px) 100vw, 171px\" \/><\/p>\n<p>Answer:<br \/>\n50.24 sq mm<\/p>\n<p>Explanation:<br \/>\nThe above-given figure is about\u00a0 50.24 sq mm<br \/>\nQuestion 2.<br \/>\nFind the perimeter and the area of the figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-4.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 4\" width=\"183\" height=\"173\" \/><\/p>\n<p>Answer:<br \/>\nperimeter of the figure = 3.16 sq in<br \/>\narea of the figure = 3.14 sq in<\/p>\n<p>Explanation:<br \/>\nperimeter of the semicircle = ( \u03c0 + 2) r<br \/>\np = (3.14 + 2 ) 1<br \/>\np = 3.16 in<br \/>\narea of the figure = \u03c0 x r x r<br \/>\narea = 3.14 x 1 x1<br \/>\narea = 3.14 in<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 3.<br \/>\n<strong>ESTIMATING PERIMETER AND AREA<\/strong><br \/>\nEstimate the perimeter and area of the figure at the right.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-5.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 5\" width=\"176\" height=\"169\" \/><\/p>\n<p>Answer:<br \/>\nThe perimeter\u00a0 and area = 30 ft<br \/>\narea = \u00a0\u03c0\u00a0 x r x r<\/p>\n<p>Explanation:<\/p>\n<p>The perimeter = ( \u03c0 + 2) r<br \/>\narea = \u00a0\u03c0\u00a0 x r x r<\/p>\n<p>Question 4.<br \/>\n<strong>FINDING PERIMETER AND AREA<\/strong><br \/>\nIdentify the shapes that make up the figure at the left. Then find the perimeter and area of the figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-6.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 6\" width=\"164\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nThe perimeter = 9.48 sq ft<br \/>\narea =\u00a0 27.36 sq ft<\/p>\n<p>Explanation:<br \/>\nThe perimeter = ( \u03c0 + 2) r<br \/>\nperimeter = 3.14 +2 x 3<br \/>\nperimeter = 9.48 sq ft<br \/>\narea = 3.14 x 3 x 3<br \/>\narea = 27.36 sq feet<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\nA farmer wants to seed and fence a section of land. Fencing costs $27 per yard. Grass seed costs $2 per square foot. How much does it cost to fence and seed the pasture?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-7.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 7\" width=\"157\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-7.png 157w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-7-150x150.png 150w\" sizes=\"(max-width: 157px) 100vw, 157px\" \/><\/p>\n<p>Answer:<br \/>\n1 m<\/p>\n<p>Explanation:<br \/>\nGiven that farmer has the fencing cost = $ 27<br \/>\nseed cost = $ 2<br \/>\n5.10 $ is used to cost for\u00a0 grass seed<br \/>\n$ 27 is used to fence = 1 m<\/p>\n<p>Question 6.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIn each room shown, you plan to put down carpet and add a wallpaper border around the ceiling. Which room needs more carpeting? more wallpaper?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-8.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 8\" width=\"319\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-8.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-8-300x112.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>Answer:<br \/>\nRoom A needs more carpeting.<\/p>\n<p>Explanation:<br \/>\nRoom A =\u00a0 10 x 11<br \/>\nwhere length = 11 , breadth = 10 given<br \/>\nRoom A = 110<br \/>\nRoom B = 12 x 8<br \/>\nB = 96<\/p>\n<h3><a id=\"Perimeters_and_Areas_of_Composite_Figures_Homework_&amp;_Practice_9.3\"><\/a>Perimeters and Areas of Composite Figures Homework &amp; Practice 9.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the area of the circle. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-9.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 9\" width=\"115\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\nArea of the circle = 50.24 sq mm<\/p>\n<p>Explanation:<br \/>\nArea of the circle = \u03c0 x r x r<br \/>\narea = 3.14 x 4 x 4<br \/>\narea = 3.14 x 16<br \/>\narea = 50.24 sq mm<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-10.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 10\" width=\"123\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\nArea of the circle = 63.585 sq ft<\/p>\n<p>Explanation:<br \/>\nArea of the plate = \u03c0 x r x r<br \/>\narea = 3.14 x 4.5 x 4.5<br \/>\narea = 3.14 x<br \/>\narea = 63.585 sq ft<\/p>\n<p><strong>Find the missing dimension. Use the scale 1 : 5.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-11.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 11\" width=\"421\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-11.png 421w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-11-300x109.png 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><\/p>\n<p>Answer:<br \/>\n3. Height = 30 ft<br \/>\n4. Length = 6 ft<br \/>\n5. Depth = 100 cm<br \/>\n6. Diameter = 2 in<\/p>\n<p>Explanation:<br \/>\n3. house : height = 6 ft , height = 30 ft given that scale = 1 : 5<br \/>\n4. garden hose : length = 6 ft , length = 20 yd<br \/>\n4. fountain : depth = 20 cm, depth = 100 cm<br \/>\n5. bicycle wheel :\u00a0 = diameter = 2 in\u00a0 diameter = 2 ft<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>ESTIMATING PERIMETER AND AREA<\/strong> You build a patio with a brick border. (See Exploration 1, p. 375.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-12.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 12\" width=\"180\" height=\"107\" \/><br \/>\nQuestion 7.<br \/>\nEstimate the perimeter of the patio.<\/p>\n<p>Answer:<br \/>\nThe perimeter of a patio = 24 units<\/p>\n<p>Explanation:<br \/>\nIn the above-given figure,<br \/>\nthe perimeter of the patio = 24<\/p>\n<p>Question 8.<br \/>\nEstimate the area of the patio.<\/p>\n<p>Answer:<br \/>\narea of the patio = \u03c0 r<\/p>\n<p><strong>ESTIMATING PERIMETER AND AREA<\/strong> Estimate the perimeter and the area of the shaded figure.<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-13.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 13\" width=\"171\" height=\"142\" \/><\/p>\n<p>Answer:<br \/>\nPerimeter = 19.5 units<br \/>\narea =13.5 units<\/p>\n<p>Explanation:<br \/>\ngiven figure is trapezoid<br \/>\nPerimeter = a + b + c + d<br \/>\narea =( (a + b) x h \/2)<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-14.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 14\" width=\"167\" height=\"137\" \/><\/p>\n<p>Answer:<br \/>\narea =(\u00a0 3 \u221a 3\/2) a square<br \/>\nperimeter = 6 a<\/p>\n<p>Explanation:<br \/>\ngiven figure is hexagon<br \/>\narea =(\u00a0 3 \u221a 3\/2) a square<br \/>\nperimeter = 6 a<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-15.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 15\" width=\"175\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\nThe perimeter = 24.6 units<br \/>\nArea of the plate = 41.1 sq units<\/p>\n<p>Explanation:<br \/>\ngiven figure is semicircle<br \/>\nThe perimeter = ( \u03c0 + 2) r<br \/>\nArea of the plate = \u03c0 x\u00a0 r x r<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-16.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 16\" width=\"180\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\nPerimeter = a + b + c + d<br \/>\narea =( (a + b) x h \/2)<\/p>\n<p>Explanation:<br \/>\ngiven figure is trapezoid<br \/>\nPerimeter = a + b + c + d<br \/>\narea =( (a + b) x h \/2)<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-17.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 17\" width=\"167\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\nPerimeter = 19 units<br \/>\narea = 24\u00a0 squnits<\/p>\n<p>Explanation:<br \/>\ngiven figure is pentagon<br \/>\nPerimeter = 5 a<br \/>\narea = (\u00a0 perimeter x apotherm \/2 )<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-18.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 18\" width=\"174\" height=\"139\" \/><\/p>\n<p>Answer:<br \/>\nPerimeter = a + b + c<br \/>\narea = (\u00a0 height x breadth \/2 )<\/p>\n<p>Explanation:<br \/>\ngiven figure is triangle<br \/>\nPerimeter = a + b + c<br \/>\narea = (\u00a0 height x breadth \/2 )<\/p>\n<p><strong>FINDING PERIMETER AND AREA<\/strong> Find the perimeter and the area of the figure.<br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-19.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 19\" width=\"152\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\narea = 137 sq m<br \/>\nperimeter = 56 m<\/p>\n<p>Explanation:<br \/>\narea of the rectangle = l x w<br \/>\nl = length, w = width<br \/>\narea = 12 x 11<br \/>\narea = 137 sq m<br \/>\nperimeter of the rectangle = 2 ( l + w)<br \/>\nperimeter = 2 (28)<br \/>\nperimeter = 56 m<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-20.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 20\" width=\"136\" height=\"122\" \/><\/p>\n<p>Answer:<br \/>\narea = 114.07 sq ft<br \/>\nperimeter = 47.4 sq ft<\/p>\n<p>Explanation:<br \/>\nArea of semicircle =( \u03c0+r x r\/2)<br \/>\narea =( 3.14 +225\/2)<br \/>\narea =(228.14\/2)<br \/>\narea = 114.07 sq ft<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) r<br \/>\nperimeter = (3.14 + 2) 15 given r= 15<br \/>\nperimeter = 3.16 x 15<br \/>\nperimeter = 47.4 sq ft<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-21.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 21\" width=\"165\" height=\"140\" \/><\/p>\n<p>Answer:<br \/>\narea = 49.5 cm<br \/>\nperimeter = 29 cm<\/p>\n<p>Explanation:<br \/>\narea of the rectangle = l x w<br \/>\nl = length, w = width<br \/>\narea = 7 x 7<br \/>\narea = 49 cm<br \/>\nperimeter of the rectangle = 2 ( l + w)<br \/>\nperimeter = 2 (14)<br \/>\nperimeter = 29 cm<\/p>\n<p>Question 18.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the perimeter of the figure. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-22.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 22\" width=\"466\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-22.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-22-300x81.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>Answer:<br \/>\nYes my friend is correct.<\/p>\n<p>Explnation:<br \/>\nperimeter = length + side +\u00a0 height + breadth + width + base<br \/>\np = 4 + 3 + 4 + 5 + 4 + 5<br \/>\np = 25 in<\/p>\n<p>Question 19.<br \/>\n<strong>LOGIC<\/strong><br \/>\nA running track has six lanes. Explain why the starting points for the six runners are staggered. Draw a diagram as part of your explanation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-23.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 23\" width=\"217\" height=\"142\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-13-300x259.png\" alt=\"\" width=\"300\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-13-300x259.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-13.png 340w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nThe starting points for the six runners are staggered because each runner can run the same distance.<\/p>\n<p>Explanation:<br \/>\nThe starting points are staggered so that each runner can run the same distance and use the same finish line.<br \/>\nthis is necessary because the circumference is different for each lane.<br \/>\nthe above-diagram shows this because the diameter is greater n the outer lanes.<\/p>\n<p>Question 20.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou run around the perimeter of the baseball field at a rate of 9 feet per second. How long does it take you to run around the baseball field?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-24.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 24\" width=\"221\" height=\"184\" \/><\/p>\n<p>Answer:<br \/>\nIt take to run around the baseball field = 1,58,962.5 sq feet<\/p>\n<p>Explanation:<br \/>\nThe area of the circle = \u03c0 x r x r<br \/>\narea = 3.14 x 225 x 225<br \/>\narea = 1,58,962.5 sq feet<\/p>\n<p>Question 21.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nThe figure at the right is made up of a square and a rectangle. Find the area of the shaded region.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-25.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 25\" width=\"284\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the shaded region =24 sq m<\/p>\n<p>Ex planation:<br \/>\nArea of triangle = ( b x h )\/2<br \/>\narea =( 8 x 7)\/ 2<br \/>\narea = 48\/2<br \/>\narea = 24 sq m<br \/>\nQuestion 22.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYour friend makes a two-dimensional model of a dividing cell as shown. The total area of the dividing cell is 350 square inches. What is the area of the shaded region?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.3-26.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles 9.3 26\" width=\"205\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the shaded region = 1.89 sq in<\/p>\n<p>Explanation :<br \/>\narea of semicircle = (\u03c0 + r x r\/2)<br \/>\narea = (3.14 + 64\/2)<br \/>\narea = ( 3.78 \/ 2)<br \/>\narea = 1.89 sq in<br \/>\nQuestion 23.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nHow can you add a figure to a composite figure without increasing its perimeter? Can this be done for all figures? Draw a diagram to support your answer.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-14.png\" alt=\"\" width=\"247\" height=\"237\" \/><\/p>\n<p>Explanation:<br \/>\nThe perimeter does not increases.<\/p>\n<h3><a id=\"Lesson_9.4_Constructing_Polygons\"><\/a>Lesson 9.4 Constructing Polygons<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using Technology to Draw Polygons<br \/>\nWork with a partner.<br \/>\na. Use geometry software to draw each polygon with the given side lengths or angle measures, if possible. Complete the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 1\" width=\"548\" height=\"439\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-1.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-1-300x240.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><br \/>\nb. Without constructing, how can you tell whether it is possible to draw a triangle given three angle measures? three side lengths? Explain your reasoning.<br \/>\nc. Without constructing, how can you tell whether it is possible to draw a quadrilateral given four angle measures? four side lengths? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nb. Yes it is possible to draw a triangle with the given three angles measures, three side lengths.<br \/>\nc. yes it is possible to draw a quadrilateral with the given 4 angle measures, four side lengths.<\/p>\n<p>Explanation:<br \/>\n1. given that sides = 4 cm , 6 cm , 7cm<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-15.png\" alt=\"\" width=\"233\" height=\"201\" \/><br \/>\n2. given that sides = 2 cm , 3 cm , 3 cm, 5 cm<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-16.png\" alt=\"\" width=\"253\" height=\"148\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Draw a triangle with the given angle measures, if possible.<\/strong><br \/>\nQuestion 1.<br \/>\n45\u00b0, 45\u00b0, 90\u00b0<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-17.png\" alt=\"\" width=\"229\" height=\"146\" \/><\/p>\n<p>Explanation:<br \/>\nThe above triangle is an equilateral triangle.<br \/>\nit forms with the given angles 45\u00b0, 45\u00b0, 90\u00b0.<\/p>\n<p>Question 2.<br \/>\n100\u00b0, 55\u00b0, 25\u00b0<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-1-300x144.png\" alt=\"\" width=\"300\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-1-300x144.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-1.png 306w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nThe above triangle is scalene\u00a0 triangle.<br \/>\nit forms with the given angles 100\u00b0, 55\u00b0, 25\u00b0.<\/p>\n<p>Question 3.<br \/>\n60\u00b0, 60\u00b0, 80\u00b0<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-2.png\" alt=\"\" width=\"216\" height=\"155\" \/><\/p>\n<p>Explanation:<br \/>\nThe above triangle is an equilateral triangle.<br \/>\nit forms with the given angles60\u00b0, 60\u00b0, 80\u00b0<\/p>\n<p>Question 4.<br \/>\nDraw a triangle with side lengths of 1 inch and 2 inches that meet at a 60\u00b0 angle.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-3.png\" alt=\"\" width=\"232\" height=\"256\" \/><\/p>\n<p>Explanation:<br \/>\nThe above triangle is a scalene triangle.<br \/>\nit forms with the given angles 60\u00b0 , 1 inch and 2 inch.<\/p>\n<p><strong>Draw a triangle with the given side lengths, if possible.<\/strong><br \/>\nQuestion 5.<br \/>\n2 cm, 2 cm, 5 cm<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-4.png\" alt=\"\" width=\"208\" height=\"151\" \/><\/p>\n<p>Explanation:<br \/>\ngiven the sides of a triangle 2cm , 2 cm , 5 cm<\/p>\n<p>Question 6.<br \/>\n4 cm, 3 cm, 3 cm<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-5.png\" alt=\"\" width=\"232\" height=\"141\" \/><\/p>\n<p>Explanation:<br \/>\ngiven that 2 sides are same and one side is different.<\/p>\n<p>Question 7.<br \/>\n1 cm, 4 cm, 5 cm<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-6-3.png\" alt=\"\" width=\"167\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-6-3.png 167w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-6-3-150x150.png 150w\" sizes=\"(max-width: 167px) 100vw, 167px\" \/><\/p>\n<p><strong>Draw a quadrilateral with the given angle measures, if possible.<\/strong><br \/>\nQuestion 8.<br \/>\n100\u00b0, 90\u00b0, 65\u00b0, 105\u00b0<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-7.png\" alt=\"\" width=\"246\" height=\"144\" \/><\/p>\n<p>Explanation:<br \/>\nThe quadrilateral formed with the given angles 100\u00b0, 90\u00b0, 65\u00b0, 105\u00b0.<\/p>\n<p>Question 9.<br \/>\n100\u00b0, 40\u00b0, 20\u00b0, 20\u00b0<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-8.png\" alt=\"\" width=\"222\" height=\"158\" \/><\/p>\n<p>Explanation:<br \/>\nThe quadrilateral formed with the given angles 100\u00b0, 40\u00b0, 20\u00b0, 20\u00b0.<\/p>\n<p>Question 9.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>DRAWING POLYGONS<\/strong> Draw a polygon with the given side lengths or angle measures, if possible.<br \/>\nQuestion 10.<br \/>\n25 mm, 36 mm, 38 mm<\/p>\n<p>Answer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-34424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-9.png\" alt=\"\" width=\"212\" height=\"126\" \/><\/p>\n<p>Explanation:<br \/>\nThe polygon formed with the given sides is a triangle.<\/p>\n<p>Question 11.<br \/>\n10\u00b0, 15\u00b0, 155\u00b0<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-7.png\" alt=\"\" width=\"246\" height=\"144\" \/><\/p>\n<p>Explanation:<br \/>\nThe polygon formed with the given sides is a triangle.<\/p>\n<p>Question 12.<br \/>\n20\u00b0, 45\u00b0, 50\u00b0, 65\u00b0<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34630\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-34-300x296.png\" alt=\"\" width=\"300\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-34-300x296.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-34.png 319w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nThe polygon formed with the given sides is a\u00a0 hexagon.<\/p>\n<p>Question 9.<br \/>\n100\u00b0, 40\u00b0, 20\u00b0, 20\u00b0<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-8.png\" alt=\"\" width=\"222\" height=\"158\" \/><\/p>\n<p>Explanation:<br \/>\nThe polygon formed with the given sides is a\u00a0 hexagon.<br \/>\nQuestion 9.<br \/>\n100\u00b0, 40\u00b0, 20\u00b0, 20\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-8.png\" alt=\"\" width=\"222\" height=\"158\" \/><br \/>\nQuestion 9.<br \/>\n100\u00b0, 40\u00b0, 20\u00b0, 20\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-8.png\" alt=\"\" width=\"222\" height=\"158\" \/><\/p>\n<p>Explanation:<br \/>\nThe polygon formed with the given sides is a\u00a0 quadrilateral.<\/p>\n<p>Question 13.<br \/>\n50\u00b0, 90\u00b0, 110\u00b0, 110\u00b0<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34631\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-35-300x142.png\" alt=\"\" width=\"300\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-35-300x142.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-35.png 372w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 14.<br \/>\n<strong>USING SIDE LENGTH<\/strong><br \/>\nCan you construct one, many, or triangle(s) with side lengths of 3 inches, 4 inches, and 8 inches? Explain.<br \/>\nAnswer:<br \/>\nWe can construct only one triangle<\/p>\n<p>Explanation:<br \/>\nGiven the side lengths of 3 inches, 4 inches, and 8 inches.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 15.<br \/>\nA triangular pen has fence lengths of 6 feet, 8 feet, and 10 feet. Create a scale drawing of the pen.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34632\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-36.png\" alt=\"\" width=\"277\" height=\"263\" \/><\/p>\n<p>Question 16.<br \/>\nThe front of a cabin is the shape of a triangle. The angles of the triangle are 40\u00b0, 70\u00b0, and 70\u00b0. Can you determine the height of the cabin? If not, what information do you need?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34633\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-37-300x191.png\" alt=\"\" width=\"300\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-37-300x191.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-37.png 310w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTwo rooftops have triangular patios. One patio has side lengths of 9 meters,10 meters, and 11 meters.\ue023e other has side lengths of 6 meters,10 meters, and 15 meters. Which patio has a greater area? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-2.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 2\" width=\"187\" height=\"185\" \/><br \/>\nAnswer:<br \/>\nThe patio which has a side length of 6 meters, 10 meters, and 15 meters.<\/p>\n<p>Explanation:<br \/>\nThe patio has a greater side length.<\/p>\n<h3><a id=\"Constructing_Polygons_Homework_&amp;_Practice_9.4\"><\/a>Constructing Polygons Homework &amp; Practice 9.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the perimeter and area of the figure.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-3.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 3\" width=\"184\" height=\"111\" \/><br \/>\nAnswer:<br \/>\narea = 12 in<br \/>\nperimeter = 14 in<\/p>\n<p>Explanation:<br \/>\narea of the rectangle = l x w<br \/>\nl = length, w = width<br \/>\narea = 4 x 3<br \/>\narea = 12 in<br \/>\nperimeter of the rectangle = 2 ( l + w)<br \/>\nperimeter = 2 (7)<br \/>\nperimeter = 14 in<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-4.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 4\" width=\"123\" height=\"111\" \/><br \/>\nAnswer:<\/p>\n<p>perimeter of the figure = 9.48 sq cm<br \/>\narea of the figure = 28.26 sq cm<\/p>\n<p>Explanation:<br \/>\nperimeter of the semicircle = ( \u03c0 + 2) r<br \/>\np = (3.14 + 2 ) 3<br \/>\np = 9.48 cm<br \/>\narea of the figure = \u03c0 x r x r<br \/>\narea = 3.14 x 3 x3<br \/>\narea = 28.26 sq cm<\/p>\n<p>Use a tree diagram to find the sample space and the total number of possible outcomes of the indicated event.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-5.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 5\" width=\"189\" height=\"254\" \/><br \/>\nQuestion 3.<br \/>\nchoosing a toothbrush<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-6.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 6\" width=\"246\" height=\"81\" \/><br \/>\nAnswer:<br \/>\nExtra soft, soft, Medium<\/p>\n<p>Explanation:<br \/>\nIn the above given figure the strength of the toothbrush = extra soft , soft , meedium<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-7.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 7\" width=\"251\" height=\"98\" \/><br \/>\nAnswer:<br \/>\nThe size of the toy hop is small, medium , large.<\/p>\n<p>Explanation:<br \/>\ngiven that the colour of the toy hoop is blue , green , orange, pink, purple , yellow.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING TECHNOLOGY TO DRAW POLYGONS<\/strong> Use geometry software to draw the polygon with the given side lengths or angle measures, if possible. (See Exploration 1, p. 381.)<br \/>\nQuestion 5.<br \/>\n30\u00b0, 65\u00b0, 85\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-7.png\" alt=\"\" width=\"246\" height=\"144\" \/><\/p>\n<p>Question 6.<br \/>\n2 in., 3 in., 5 in.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-9.png\" alt=\"\" width=\"212\" height=\"126\" \/><\/p>\n<p>Question 7.<br \/>\n80\u00b0, 90\u00b0, 100\u00b0, 110\u00b0<br \/>\nAnswer:<br \/>\nNot possible.<\/p>\n<p>Question 8.<br \/>\n2 cm, 2 cm, 5 cm, 5 cm<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34628\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-32-300x133.png\" alt=\"\" width=\"300\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-32-300x133.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-32.png 355w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>CONSTRUCTING TRIANGLES USING ANGLE MEASURES<\/strong> Draw a triangle with the given angle measures, if possible.<br \/>\nQuestion 9.<br \/>\n40\u00b0, 50\u00b0, 90\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-8.png\" alt=\"\" width=\"222\" height=\"158\" \/><\/p>\n<p>Question 10.<br \/>\n20\u00b0, 40\u00b0, 120\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-8.png\" alt=\"\" width=\"222\" height=\"158\" \/><\/p>\n<p>Question 11.<br \/>\n38\u00b0, 42\u00b0, 110\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-8.png\" alt=\"\" width=\"222\" height=\"158\" \/><\/p>\n<p>Question 12.<br \/>\n54\u00b0, 60\u00b0, 66\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-8.png\" alt=\"\" width=\"222\" height=\"158\" \/><\/p>\n<p>Question 13.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend determines whether he can draw a triangle with angle measures of 10\u00b0, 40\u00b0, and 130\u00b0. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-8.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 8\" width=\"281\" height=\"127\" \/><br \/>\nAnswer:<br \/>\nYes .<\/p>\n<p>Explanation:<br \/>\nyes we cannot draw the triangle with the angle measures of 10, 40, 130<\/p>\n<p><strong>CONSTRUCTING TRIANGLES USING ANGLES AND SIDES<\/strong> Draw a triangle with the given description.<br \/>\nQuestion 14.<br \/>\nside lengths of 1 inch and 2 inches meet at a 50\u00b0 angle<br \/>\nAnswer:<br \/>\nyes.<\/p>\n<p>Explanation:<br \/>\nwe can draw a triangle with 1 inch 2 inch that meets at\u00a0 50 degrees.<\/p>\n<p>Question 15.<br \/>\nside lengths of 7 centimeters and 9 centimeters meet at a 120\u00b0 angle<br \/>\nAnswer:<br \/>\nyes.<\/p>\n<p>Explanation:<br \/>\nwe can draw a triangle with 7 cm 9 cm that meets at\u00a0 120 degrees.<\/p>\n<p>Question 16.<br \/>\na 95\u00b0 angle connects to a 15\u00b0 angle by a side of length 2 inches<br \/>\nAnswer:<br \/>\nno.<\/p>\n<p>Explanation:<br \/>\nwe cannot draw a triangle with 2 inches 15 degrees that meets at\u00a0 120 degrees.<\/p>\n<p>Question 17.<br \/>\na 70\u00b0 angle connects to a 70\u00b0 angle by a side of length 4 centimeters<br \/>\nAnswer:<br \/>\nyes.<\/p>\n<p>Explanation:<br \/>\nwe can draw an angle with 4 cm\u00a0 70 degrees that meets at\u00a0 120 degrees.<\/p>\n<p><strong>CONSTRUCTING TRIANGLES USING SIDE LENGTHS<\/strong> Draw a triangle with the given side lengths, if possible.<br \/>\nQuestion 18.<br \/>\n4 in., 5 in., 10 in.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-31-300x104.png\" alt=\"\" width=\"300\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-31-300x104.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-31.png 499w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 19.<br \/>\n10 mm, 30 mm, 50 mm<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-9.png\" alt=\"\" width=\"212\" height=\"126\" \/><\/p>\n<p>Question 20.<br \/>\n5 cm, 5 cm, 8 cm<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34625\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-29-1.png\" alt=\"\" width=\"216\" height=\"143\" \/><\/p>\n<p>Question 21.<br \/>\n8 mm, 12 mm, 13 mm<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34626\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-30-300x255.png\" alt=\"\" width=\"300\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-30-300x255.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-30.png 406w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nCan you construct a triangular case using two pieces of wood that are 12 inches long and one piece of wood that is 25 inches long? Explain.<br \/>\nAnswer:<br \/>\nYes we can construct a triangle .<\/p>\n<p>Explanation:<br \/>\nWe can costruct the triangle by using two pieces of wood that are 12 inches long and the one piece of wood is 25 inches.<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nCan you construct a warning triangle using three pieces of plastic that are each 6 inches long? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-9.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 9\" width=\"104\" height=\"87\" \/><br \/>\nAnswer:<br \/>\nYes.<\/p>\n<p>Explanation:<br \/>\nwe can construct the three pieces of plastic by using 3 6 inches long.<\/p>\n<p>Question 24.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYou are constructing a triangle. You draw the first angle, as shown. Your friend says that you must be constructing an acute triangle. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-10.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 10\" width=\"225\" height=\"124\" \/><br \/>\nAnswer:<br \/>\nYes my friend is correct.<\/p>\n<p>Explanation:<br \/>\nit is a acute angle triangle.<\/p>\n<p><strong>USING ANGLES AND SIDES<\/strong> Determine whether you can construct one, many, or no triangle(s) with the given description. Explain your reasoning.<br \/>\nQuestion 25.<br \/>\na triangle with one angle measure of 60and one side length of 4 centimeters<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-28-1.png\" alt=\"\" width=\"184\" height=\"131\" \/><\/p>\n<p>Explanation:<br \/>\nwe cannot construct one trinangle with the help of given sidelengths.<\/p>\n<p>Question 26.<br \/>\na scalene triangle with side lengths of 3 centimeters and 7 centimeters<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-28-1.png\" alt=\"\" width=\"184\" height=\"131\" \/><\/p>\n<p>Question 27.<br \/>\nan isosceles triangle with two side lengths of 4 inches that meet at an 80\u00b0 angle<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-38.png\" alt=\"\" width=\"251\" height=\"155\" \/><\/p>\n<p>Question 28.<br \/>\na triangle with one angle measure of 60\u00b0, one angle measure of 70\u00b0, and a side length of 10 centimeters between the two angles<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34622\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-27-1-300x188.png\" alt=\"\" width=\"300\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-27-1-300x188.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-27-1.png 392w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 29.<br \/>\na triangle with one angle measure of 20\u00b0, one angle measure of 35\u00b0, and a side of length 3 inches that is between the two angles<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34618\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-26-2.png\" alt=\"\" width=\"282\" height=\"81\" \/><\/p>\n<p>Question 29.<br \/>\n<strong>REASONING<\/strong><br \/>\nA triangle is shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-11.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 11\" width=\"129\" height=\"128\" \/><br \/>\na. Construct a triangle with side lengths twice those of the triangle shown. Does the new triangle have the same angle measures?<br \/>\nb. How can you change the side lengths of the triangle so that the measure of \u2220A increases?<br \/>\nAnswer:<br \/>\na. Yes the new triangle have the same angle.<br \/>\nb. angle A increases .<\/p>\n<p>Explanation:<br \/>\nGiven that the triangle with side lengths twice those of the triangle shown.<br \/>\nIf we can change the side lengths of triangle .<\/p>\n<p><strong>CONSTRUCTING QUADRILATERALS<\/strong> Draw a quadrilateral with the given angle measures, if possible.<br \/>\nQuestion 31.<br \/>\n60\u00b0, 60\u00b0, 120\u00b0, 120\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-26-300x187.png\" alt=\"\" width=\"300\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-26-300x187.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-26.png 389w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 32.<br \/>\n50\u00b0, 60\u00b0, 110\u00b0, 150\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34615\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-24-1-300x203.png\" alt=\"\" width=\"300\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-24-1-300x203.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-24-1.png 394w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 33.<br \/>\n20\u00b0, 30\u00b0, 150\u00b0, 160\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34614\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-23-1-300x248.png\" alt=\"\" width=\"300\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-23-1-300x248.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-23-1.png 430w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 34.<br \/>\n10\u00b0, 10\u00b0, 10\u00b0, 150\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34611\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-22-1-300x172.png\" alt=\"\" width=\"300\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-22-1-300x172.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-22-1.png 554w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven angles are 10 degrees, 10 degrees, 10 degrees, 10 degrees.<\/p>\n<p><strong>CONSTRUCTING SPECIAL QUADRILATERALS<\/strong> Construct a quadrilateral with the given description.<br \/>\nQuestion 35.<br \/>\na rectangle with side lengths of 1 inch and 2 inches<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34610\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-21-1.png\" alt=\"\" width=\"229\" height=\"124\" \/><\/p>\n<p>Question 36.<br \/>\na kite with side lengths of 4 centimeters and 7 centimeters<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34609\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-20-1-300x150.png\" alt=\"\" width=\"300\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-20-1-300x150.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-20-1.png 305w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 37.<br \/>\na trapezoid with base angles of 40\u00b0<br \/>\nAnswer:<br \/>\nA<img loading=\"lazy\" class=\"alignnone size-full wp-image-34608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-28.png\" alt=\"\" width=\"268\" height=\"148\" \/>nswer<\/p>\n<p>Question 38.<br \/>\na rhombus with side lengths of 10 millimeters<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34607\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-27.png\" alt=\"\" width=\"284\" height=\"188\" \/><\/p>\n<p>Question 39.<br \/>\n<strong>REASONING<\/strong><br \/>\nA quadrilateral has side lengths of 6 units, 2 units, and 3 units as shown. How many quadrilaterals can be formed given a fourth side with a fixed length? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-12.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 12\" width=\"162\" height=\"95\" \/><br \/>\nAnswer:<br \/>\n2 quadrilaterals can be formed.<\/p>\n<p>Explanation:<br \/>\nGiven that the quadrilateral has side lengths of 6 units, 2 units, and 3 units.<br \/>\nso 2 quadrilaterals can be formed.<\/p>\n<p>Question 40.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhat types of quadrilaterals can you form using four side lengths of 7 units? Use drawings to support your conclusion.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-26-300x187.png\" alt=\"\" width=\"300\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-26-300x187.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-26.png 389w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 41.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA triangular section of a farm is enclosed by fences that are 2 meters, 6 meters, and 7 meters long. Estimate the area of the section.<br \/>\nAnswer:<br \/>\nArea of the section = 12 sq meters.<\/p>\n<p>Question 42.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA chemical spill expert sets up a triangular caution zone using cones. Cones A and B are 14 meters apart. Cones B and C are 22 meters apart. Cones A and C are 34 meters apart. Estimate the area of the caution zone.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-13.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 13\" width=\"263\" height=\"183\" \/><br \/>\nAnswer:<br \/>\nArea of the area of the caution Zone = 308 sq meters.<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = l x b<br \/>\narea = 22 x 14<br \/>\narea = 308 sq meters.<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA search region is in the shape of an equilateral triangle. The measure of one side of the region is 20 miles. Make a scale drawing of the search region. Estimate the area of the search region.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34604\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-25.png\" alt=\"\" width=\"258\" height=\"222\" \/><\/p>\n<p>Explanation:<br \/>\nGiven that the equilateral triangle .<\/p>\n<p>Question 44.<br \/>\n<strong>REASONING<\/strong><br \/>\nA triangle has fixed side lengths of 2 and 14.<br \/>\na. How many triangles can you construct? Use the figure below to explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-14.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 9 Geometric Shapes and Angles 9.4 14\" width=\"394\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-14.png 394w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.4-14-300x85.png 300w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><br \/>\nb. Is the unknown side length of the triangle also fixed? Explain.<br \/>\nAnswer:<br \/>\nWe can construct 14 triangles.<br \/>\nb. No the side length of the triangle cannot fixed.<\/p>\n<p>Explanation:<br \/>\na. We can construct 14 triangles.<br \/>\nb. No the side length of the triangl cannot fixed.<\/p>\n<h3><a id=\"Lesson_9.5_Finding_Unknown_Angle_Measures\"><\/a>Lesson 9.5 Finding Unknown Angle Measures<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using Rules About Angles<br \/>\nWork with a partner. The diagram shows pairs of angles and vertical angles. Vertical angles cannot be adjacent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 1\" width=\"413\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-1.png 413w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-1-300x92.png 300w\" sizes=\"(max-width: 413px) 100vw, 413px\" \/><br \/>\na. Which pair(s) of angles are adjacent angles? Explain.<br \/>\nb. Which pair(s) of angles are vertical angles? Explain.<br \/>\nc. Without using a protractor, \ufb01nd the values of x, y, and z. Explain your reasoning.<br \/>\nd. Make a conjecture about the measures of any two vertical angles.<br \/>\ne. Test your conjecture in part(d) using the diagram below. Explain why your conjecture is or is not true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 2\" width=\"520\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-2.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-2-300x98.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><br \/>\nAnswer:<br \/>\nA. \u2220ACD, \u2220AEB<br \/>\nb. \u2220ACD, \u2220AEB<br \/>\nc. 125<br \/>\nd. \u2220ACD, \u2220AEB<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 3\" width=\"188\" height=\"170\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nName a pair of (a) adjacent angles, (b) complementary angles, (c) supplementary angles, and (d) vertical angles in the figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 4\" width=\"167\" height=\"133\" \/><br \/>\nAnswer:<br \/>\na. \u2220JKL, \u2220JKQ, . \u2220MNJ,. \u2220PJN<br \/>\nb. \u2220JKQ<br \/>\nc. \u2220JNK, \u2220 JPL. \u2220JMQ<br \/>\nD. \u2220JMQ, \u2220JPL.<\/p>\n<p>Explanation:<br \/>\nThe above angles are adjacent, vertical, supplementary,complementary.<\/p>\n<p><strong>Classify the pair of angles. Then find the value of x.<\/strong><br \/>\nQuestion 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 5\" width=\"135\" height=\"80\" \/><br \/>\nAnswer:<br \/>\nx = 95 \u02da<\/p>\n<p>Explanation:<br \/>\nx = (180 &#8211; 85)<br \/>\nx = 95 \u02da<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27962\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 6\" width=\"128\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nx =\u00a0 180\u00a0\u02da<\/p>\n<p>Explanation:<br \/>\nx = 180\u00a0\u02da<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27963\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 7\" width=\"119\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nx = 30\u00a0\u02da<\/p>\n<p>Explanation:<br \/>\n(2x &#8211; 3) = 60<br \/>\n2x = (60\/3)<br \/>\n2x = 20<br \/>\nx = 10<\/p>\n<p><strong>Find the measure of the indicated angle in the diagram.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27964\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-8.1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 8.1\" width=\"137\" height=\"159\" \/><br \/>\nQuestion 5.<br \/>\n\u2220NJM<br \/>\nAnswer:<br \/>\n12 x \u02da<\/p>\n<p>Question 6.<br \/>\n\u2220KJP<br \/>\nAnswer:<br \/>\n16 x \u02da<\/p>\n<p>Question 7.<br \/>\n\u2220KJM<br \/>\nAnswer:<br \/>\n6x \u02da<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 8.<br \/>\n<strong>NAMING ANGLES<\/strong><br \/>\nName a pair of (a) adjacent angles, (b) complementary angles, (c) supplementary angles, and (d) vertical angles in the figure at the left.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 8\" width=\"166\" height=\"139\" \/><br \/>\nAnswer:<br \/>\na. \u2220ABC<br \/>\nb. \u2220ABD<br \/>\nc. \u2220ABE<br \/>\nd. \u2220ABE<\/p>\n<p>Explanation:<br \/>\nThe above angles are adjacent, vertical, supplementary,complementary.<\/p>\n<p><strong>FINDING ANGLE MEASURES Find the value of x.<\/strong><br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27966\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 9\" width=\"138\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nx = 60\u02da<\/p>\n<p>Explanation:<br \/>\n4x = x<br \/>\n4x &#8211; x = 180<br \/>\n3x = 180<br \/>\nx = 60\u02da<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27967\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-10.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 10\" width=\"150\" height=\"118\" \/><br \/>\nAnswer:<br \/>\nx = 12.5\u02da<\/p>\n<p>Explanation:<br \/>\n2x\u00a0 &#8211; 10= 2x + 40<br \/>\n4x\u00a0 = 50<br \/>\nx = 12.5\u02da<\/p>\n<p>Question 11.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich pair of angles does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27968\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 11\" width=\"613\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-11.png 613w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-11-300x55.png 300w\" sizes=\"(max-width: 613px) 100vw, 613px\" \/><br \/>\nAnswer:<br \/>\n\u2220FBA, \u2220EBD does not belong with the other three.<\/p>\n<p>Explanation:<br \/>\nthe 3 angles are different measures,<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 12.<br \/>\nWhat is the angle between any two windmill blades in the windmill at the left? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 12\" width=\"157\" height=\"210\" \/><\/p>\n<p>Answer:<br \/>\nThe angle between any two wind mills blades in the windmill at the left = 60 \u00b0<\/p>\n<p>Explanation:<br \/>\n60 + 60 + 60 = 180<\/p>\n<p>Question 13.<br \/>\nA hockey puck strikes a wall at an angle of 30\u00b0. The puck then travels away from the wall at the same angle. Find the value of y. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 13\" width=\"247\" height=\"96\" \/><br \/>\nAnswer:<br \/>\ny = 150 \u00b0<\/p>\n<p>Explanation:<br \/>\nIn the above figure said that hockey puck strikes a wall at an angle of 30 \u00b0.<br \/>\nso 180 &#8211; 30 = 150<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe laptop screen turns off when the angle between the keyboard and the screen is less than 20\u00b0. How many more degrees can the laptop screen close before the screen turns off?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27971\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-14.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 14\" width=\"156\" height=\"116\" \/><br \/>\nAnswer:<br \/>\nThe laptop screen close before the screen turns off = 60 degrees.<\/p>\n<p>Explanation:<br \/>\n(z + 40) = (z &#8211; 20)<br \/>\nz &#8211; z = (-\u00a0 20 -40)<br \/>\nz = -60<\/p>\n<h3><a id=\"Finding_Unknown_Angle_Measures_Homework_&amp;_Practice_9.5\"><\/a>Finding Unknown Angle Measures Homework &amp; Practice 9.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Draw a triangle with the given side lengths, if possible.<\/strong><br \/>\nQuestion 1.<br \/>\n1 in., 3 in., 4 in.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-21.png\" alt=\"\" width=\"159\" height=\"162\" \/><\/p>\n<p>Explanation:<br \/>\nIn the above question , they said to draw 1 in, 3 in, 4 in.<\/p>\n<p>Question 2.<br \/>\n4 cm, 4 cm, 7 cm<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-22-300x131.png\" alt=\"\" width=\"300\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-22-300x131.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-22.png 364w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Solve the inequality. Graph the solution.<br \/>\nQuestion 3.<br \/>\n&#8211; 8y \u2264 40<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34600\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-23.png\" alt=\"\" width=\"265\" height=\"142\" \/><\/p>\n<p>Explanation:<br \/>\n&#8211; 8y \u2264 40<br \/>\ny = (40\/8)<br \/>\ny = 5<\/p>\n<p>Question 4.<br \/>\n1.1z &gt; &#8211; 3.3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34601\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-24-300x114.png\" alt=\"\" width=\"300\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-24-300x114.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-24.png 315w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nz = 3.3<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{1}{3}\\)x \u2265 2.5<br \/>\nAnswer:<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING RULES ABOUT ANGLES<\/strong> The diagram shows pairs of adjacent vertical angles and angles. B(See Exploration 1, p. 389.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 15\" width=\"135\" height=\"132\" \/><br \/>\nQuestion 6.<br \/>\nWhich pair(s) of angles are adjacent angles? Explain.<br \/>\nAnswer:<br \/>\nangle AEC, angle ABD.<\/p>\n<p>Explanation:<br \/>\nIn the above given figure angle AEC, angle ABD are adjacent.<\/p>\n<p>Question 7.<br \/>\nWhich pair(s) of angles are vertical angles? Explain.<br \/>\nAnswer:<br \/>\nangle ABC, angle ADE<\/p>\n<p>Explanation:<br \/>\nIn the above given figure angle AEC, angle ABD are adjacent.<\/p>\n<p><strong>NAMING ANGLES<\/strong> Use the figure shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-16.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 16\" width=\"167\" height=\"117\" \/><br \/>\nQuestion 8.<br \/>\nName a pair of adjacent angles.<br \/>\nAnswer:<br \/>\n\u2220ADC, \u2220AEF, \u2220ABC<\/p>\n<p>Question 9.<br \/>\nName a pair of complementary angles.<br \/>\nAnswer:<br \/>\n\u2220ADE, \u2220ABD<\/p>\n<p>Question 10.<br \/>\nName a pair of supplementary angles.<br \/>\nAnswer:<br \/>\n\u2220ABE, \u2220ACF<\/p>\n<p>Question 11.<br \/>\nName a pair of vertical angles.<br \/>\nAnswer:<br \/>\n\u2220AEF, \u2220ABC<\/p>\n<p>Question 12.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend names a pair of angles with the same measure. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-17.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 17\" width=\"203\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nyes my friend is correct<\/p>\n<p>Explanation:<br \/>\nThe angles both have the same measure.<\/p>\n<p><strong>ADJACENT AND VERTICAL ANGLES<\/strong> Tell whether the angles are adjacent, vertical, or neither. Explain.<br \/>\nQuestion 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-18.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 18\" width=\"104\" height=\"98\" \/><br \/>\nAnswer:<br \/>\nvertical.<\/p>\n<p>Explanation:<br \/>\nThe given angles are vertical.<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-19.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 19\" width=\"138\" height=\"82\" \/><br \/>\nAnswer:<br \/>\nAdjacent.<\/p>\n<p>Explanation:<br \/>\nThe given angles are adjacent.<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-20.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 20\" width=\"138\" height=\"70\" \/><\/p>\n<p>Answer:<br \/>\nAdjacent, vertical<\/p>\n<p>Explanation:<br \/>\nThe given angles are adjacent, vertical.<\/p>\n<p><strong>COMPLEMENTARY AND SUPPLEMENTARY ANGLES<\/strong> Tell whether the angles are complementary supplementary, or neither. Explain.<br \/>\nQuestion 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-21.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 21\" width=\"149\" height=\"96\" \/><br \/>\nAnswer:<br \/>\nThe angles are neither complementary nor supplementary.<\/p>\n<p>Explanation:<br \/>\ncomplementary = 90 degree<br \/>\nsupplementary = 180 degree<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-22.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 22\" width=\"107\" height=\"95\" \/><br \/>\nAnswer:<br \/>\nThe angles are complementary.<\/p>\n<p>Explanation:<br \/>\ncomplementary = 90 degree<br \/>\nsupplementary = 180 degree<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-23.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 23\" width=\"143\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nThe angles are complementary.<\/p>\n<p>Explanation:<br \/>\ncomplementary = 90 degree<br \/>\nsupplementary = 180 degree<\/p>\n<p>Question 19.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend names a pair of supplementary angles. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-24.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 24\" width=\"357\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-24.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-24-300x117.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><br \/>\nAnswer:<br \/>\nyes my friend is correct.<\/p>\n<p>Explanation:<br \/>\nangle LMN and angle PMQ are supplementary angles.<\/p>\n<p><strong>USING PAIRS OF ANGLES<\/strong> Classify the pair of angles. Then find the value of x.<br \/>\nQuestion 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-25.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 25\" width=\"116\" height=\"106\" \/><br \/>\nAnswer:<br \/>\nAcute angle.<br \/>\nx = 145<\/p>\n<p>Explanation:<br \/>\nx = (180 &#8211; 35)<br \/>\nx = 35<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-26.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 26\" width=\"163\" height=\"86\" \/><br \/>\nAnswer:<br \/>\nverticle\u00a0angle.<br \/>\nx = 52<\/p>\n<p>Explanation:<br \/>\nx = (180 &#8211; 128)<br \/>\nx = 52<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-27.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 27\" width=\"161\" height=\"89\" \/><br \/>\nAnswer:<br \/>\nobtuse angle.<br \/>\nx = 63<\/p>\n<p>Explanation:<br \/>\nx = (180 &#8211; 117)<br \/>\nx = 63<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-28.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 28\" width=\"150\" height=\"80\" \/><br \/>\nAnswer:<br \/>\nintersection angles<br \/>\nx = 25<\/p>\n<p>Explanation:<br \/>\n(4x &#8211; 25) = 75<br \/>\n4x = 75 + 25<br \/>\n4x = 100<br \/>\nx = (100\/4)<br \/>\nx = 25<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-29.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 29\" width=\"101\" height=\"89\" \/><br \/>\nAnswer:<br \/>\nx = 15<\/p>\n<p>Explanation:<br \/>\n2x = 30<br \/>\nx = (30\/2)<br \/>\nx = 15<br \/>\n4x = 60<br \/>\nx = (60\/4)<br \/>\nx = 15<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-30.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 30\" width=\"160\" height=\"89\" \/><br \/>\nAnswer:<br \/>\nx = 3.33<\/p>\n<p>Explanation:<br \/>\n(x + 20 ) = 7 x<br \/>\n20 = 7x &#8211; x<br \/>\n20 = 6x<br \/>\nx = (20\/6)<br \/>\nx = 3.33<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-31.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 31\" width=\"139\" height=\"107\" \/><br \/>\nAnswer:<br \/>\nx = 15<\/p>\n<p>Explanation:<br \/>\n3x = 45<br \/>\nx = (45\/3)<br \/>\nx = 15<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-32.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 32\" width=\"119\" height=\"92\" \/><br \/>\nAnswer:<br \/>\nx = 20<\/p>\n<p>Explanation:<br \/>\n(x &#8211; 20 ) = x<br \/>\n20 = x &#8211; x<br \/>\nx = 20<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-33.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 33\" width=\"161\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nx = 25<\/p>\n<p>Explanation:<br \/>\n(3x + 25) = 2x<br \/>\n3x &#8211; 2x = 25<br \/>\nx = 25<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nWhat is the measure of each angle formed by the intersection? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-34.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 34\" width=\"189\" height=\"141\" \/><br \/>\nAnswer:<br \/>\nangle 2 = 50\u00b0<br \/>\nangle 3 = 40\u00b0<br \/>\nangle 1 = 40\u00b0<\/p>\n<p>Explanation:<br \/>\nIn the above figure the angle 4 is given.<\/p>\n<p>Question 30.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA tributary joins a river at an angle x. Find the value of x. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-35.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 35\" width=\"286\" height=\"124\" \/><br \/>\nAnswer:<br \/>\nx = 21<\/p>\n<p>Explanation:<br \/>\n(2x + 21 ) = x<br \/>\n2x &#8211; x = 21<br \/>\nx = 21<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe iron cross is a skiing trick in which the tips of the skis are crossed while the skier is airborne. Find the value of x in the iron cross shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-36.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 36\" width=\"181\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nThe value of x in the iron cross = 43<\/p>\n<p>Explanation:<br \/>\n(2x + 41) = 127<br \/>\n2x = 127 &#8211; 41<br \/>\n2x = 86<br \/>\nx = 43<\/p>\n<p><strong>FINDING ANGLE MEASURES<\/strong> Find all angle measures in the diagram.<br \/>\nQuestion 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-37.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 37\" width=\"152\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-37.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-37-150x104.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer:<br \/>\nx = 90\u02da<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-38.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 38\" width=\"154\" height=\"113\" \/><br \/>\nAnswer:<br \/>\n23.33<\/p>\n<p>Explanation:<br \/>\n(3x + 5) = 75<br \/>\n3x = 75 &#8211; 5<br \/>\n3x = 70<br \/>\nx = (70\/3)<br \/>\nx = 23.33<\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-39.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 39\" width=\"144\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nx = 68<br \/>\nx = 67<\/p>\n<p>Explanation:<br \/>\n(2x + 4) = 140<br \/>\n2x = (140 &#8211; 4)<br \/>\n2x = 136<br \/>\nx = (136\/2)<br \/>\nx = 68<br \/>\n(2x + 6) = 140<br \/>\n2x = (140 &#8211; 6)<br \/>\n2x = 134<br \/>\nx = (134\/2)<br \/>\nx = 67<\/p>\n<p><strong>OPEN-ENDED<\/strong> Draw a pair of adjacent angles with the given description.<br \/>\nQuestion 35.<br \/>\nBoth angles are acute.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34591\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-18.png\" alt=\"\" width=\"209\" height=\"109\" \/><\/p>\n<p>Question 36.<br \/>\nOne angle is acute, and one is obtuse.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34592\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-19.png\" alt=\"\" width=\"263\" height=\"182\" \/><\/p>\n<p>Question 37.<br \/>\nThe sum of the angle measures is 135\u00b0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34593\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-20-300x126.png\" alt=\"\" width=\"300\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-20-300x126.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-20.png 417w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>REASONING<\/strong> Copy and complete each sentence with always, sometimes, or never.<br \/>\nQuestion 38.<br \/>\nIf x and y are complementary angles, then both x and y are________ acute.<br \/>\nAnswer:<br \/>\nRight acute.<\/p>\n<p>Explanation:<br \/>\nif x and y are complimentary then the x and y are right acute.<\/p>\n<p>Question 39.<br \/>\nIf x and y are supplementary angles, then is x ________ acute.<br \/>\nAnswer:<br \/>\nleft acute.<\/p>\n<p>Explanation:<br \/>\nif x and y are complimentary then the x and y are right acute.<\/p>\n<p>Question 40.<br \/>\nIf x is a right angle, then is x ________ acute.<br \/>\nAnswer:<br \/>\nRight acute.<\/p>\n<p>Explanation:<br \/>\nif x and y are complimentary then the x and y are right acute.<\/p>\n<p>Question 41.<br \/>\nIf x and y are complementary angles, then x and y are ________ adjacent.<br \/>\nAnswer:<br \/>\nRight adjacent.<\/p>\n<p>Explanation:<br \/>\nif x and y are complimentary then the x and y are right adjacent.<\/p>\n<p>Question 42.<br \/>\nIf x and y are supplementary angles, then x and y are _______ vertical.<br \/>\nAnswer:<br \/>\nleft vertical.<\/p>\n<p>Explanation:<br \/>\nif x and y are supplementary then the x and y are left vertical.<\/p>\n<p>Question 43.<br \/>\n<strong>REASONING<\/strong><br \/>\nDraw a figure in which \u22201 and \u22202 are acute vertical angles, \u22203 is a right angle adjacent to \u22202, and the sum of the measure of \u22201 and the measure of \u22204 is 180\u00b0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34590\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-17-300x113.png\" alt=\"\" width=\"300\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-17-300x113.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/geometry-17.png 419w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nDescribe the relationship between the two angles represented by the graph shown at the right.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-40.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 40\" width=\"184\" height=\"169\" \/><br \/>\nAnswer:<br \/>\n90\u00b0<\/p>\n<p>Explanation:<br \/>\nThe relationship between the two angles represented by the graph =90\u00b0<\/p>\n<p>Question 45.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nConsider the figure shown at the left. Use a ruler to extend both rays into lines. What do you notice about the three new angles that are formed?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-41.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 41\" width=\"119\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nThe 3 angles that are formed = 30\u00b0, 60\u00b0, 90\u00b0<\/p>\n<p>Explanation:<br \/>\nThe given angles are right angles.<\/p>\n<p>Question 46.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nGive an example of an angle that can be a supplementary angle but cannot be a complementary angle to another angle. Explain.<br \/>\nAnswer:<br \/>\nAcute angle<\/p>\n<p>Question 47.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe vanishing point of the picture is represented by point B.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-42.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 42\" width=\"222\" height=\"154\" \/><br \/>\na. The measure of \u2220ABD is 6.2 times greater than the measure of \u2220CBD. Find the measure of \u2220CBD.<br \/>\nb. \u2220FBE and \u2220EBD are congruent. Find the measure of \u2220FBE.<br \/>\nAnswer:<br \/>\na. The measure of\u00a0 \u2220CBD = 30\u00b0<br \/>\nb. The measure of \u2220FBE = 60\u00b0<\/p>\n<p>Explanation:<br \/>\nGiven that the measure of \u2220ABD is 6.2 times greater than the measure of \u2220CBD\u00a0 = 30\u00b0<br \/>\n\u2220FBE and \u2220EBD are congruent so \u2220FBE = 60\u00b0<\/p>\n<p>Question 48.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?<br \/>\nAnswer:<br \/>\nThe measure of the larger angle = 3<\/p>\n<p>Explanation:<br \/>\ngiven that, the measures of two complementary angles have a ratio = 3 : 2<\/p>\n<p>Question 49.<br \/>\n<strong>REASONING<\/strong><br \/>\nTwo angles are vertical angles. What are their measures if they are also complementary angles? supplementary angles?<br \/>\nAnswer:<br \/>\nwhen two angles are vertical.<br \/>\ncomplementary angles = Two angles are called complementary when their measures add to 90\u00b0<br \/>\nsupplementary angles = two angles are called supplementary when their measures add to 180\u00b0<\/p>\n<p>Question 50.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nFind the values of x and y.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-9.5-43.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 9 Geometric Shapes and Angles 9.5 43\" width=\"167\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nx = 2.857<br \/>\ny = 2<br \/>\nx = 4<\/p>\n<p>Explanation:<br \/>\n7\u00a0 x = 20<br \/>\nx = (20\/7)<br \/>\nx = 2.857<br \/>\n2y = 20<br \/>\ny = (20\/10)<br \/>\ny\u00a0 = 2<br \/>\n5x = 20<br \/>\nx = (20\/5)<br \/>\nx = 4<\/p>\n<h3><a id=\"Geometric_Shapes_and_Angles_Connecting_Concepts\"><\/a>Geometric Shapes and Angles Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><br \/>\nQuestion 1.<br \/>\nA dart is equally likely to hit any point on the board shown. Find the theoretical probability that a dart hitting the board scores 100 points.<br \/>\nUnderstand the problem.<br \/>\nYou are given the dimensions of a circular dartboard. You are asked to find the theoretical probability of hitting the center circle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cc-1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cc 1\" width=\"188\" height=\"164\" \/><br \/>\nMake a plan.<br \/>\nFind the area of the center circle and the area of the entire dart board. To find the theoretical probability of scoring 100 points, divide the area of the center circle by the area of the entire dart board.<br \/>\nSolve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<br \/>\nAnswer:<br \/>\nArea of center =31,400 sq in<br \/>\narea of entire dart board = 1,962.5 sq in<\/p>\n<p>Explanation:<br \/>\nArea of center circle = \u03c0 r \u00b2<br \/>\na = 3.14 x 100 x 100<br \/>\na = 31,400\u00a0 sq in<br \/>\narea of entire dart board =\u00a0 \u03c0 r \u00b2<br \/>\na = 3.14 x 25 x 25<br \/>\na = 3.14 x 625<br \/>\na = 1,962.5 sq in<\/p>\n<p>Question 2.<br \/>\nA scale drawing of a window is shown. Find the perimeter and the area of the actual window. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cc-2.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cc 2\" width=\"156\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nArea of semicircle = 1.695sq ft<br \/>\nperimeter of semicircle = 1.58 sq ft<\/p>\n<p>Explanation:<br \/>\narea of the semicircle = ( \u03c0 + r x r \/2)<br \/>\ns . c = (3.14 + 0.5 x 0.5 \/2)<br \/>\ns. c = (3.14 + 0.25 \/2)<br \/>\ns . c = (3.39 \/2<br \/>\ns. c = 1.695 sq ft<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) x r<br \/>\np= 3.14 + 2 x 0.5<br \/>\np = 3.16 x 0.5<br \/>\np = 1.58 sq ft<\/p>\n<p>Question 3.<br \/>\n\u2220CAD makes up 20% of a pair of supplementary angles. Find the measure of \u2220DAE. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cc-3.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cc 3\" width=\"258\" height=\"136\" \/><br \/>\nAnswer:<br \/>\n\u2220DAE = 30 %<\/p>\n<p>Explanation:<br \/>\nGiven that \u2220CAD = 20%<br \/>\nso<br \/>\n\u2220DAE = 30 %<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Finding the Area and Perimeter of a Track<br \/>\nAt the beginning of the this chapter, you watched a STEAM video called \u201cTrack and Field\u201d. You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cc-4.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cc 4\" width=\"337\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cc-4.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cc-4-300x149.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<h3><a id=\"Geometric_Shapes_and_Angles_Chapter_Review\"><\/a>Geometric Shapes and Angles Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the definition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 1\" width=\"590\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-1.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-1-300x42.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use a Four Square to organize information about a concept. Each of the four squares can be a category, such as definition, vocabulary, example, non-example, words, algebra, table, numbers, visual, graph, or equation. Here is an example of a Four Square for circumference.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-2.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 2\" width=\"471\" height=\"299\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-2.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-2-300x190.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><\/p>\n<p>Choose and complete a graphic organizer to help you study each topic.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-3.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 3\" width=\"287\" height=\"319\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-3.png 287w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-3-270x300.png 270w\" sizes=\"(max-width: 287px) 100vw, 287px\" \/><br \/>\n1. area of a circle<br \/>\n2. semicircle<br \/>\n3. composite figure<br \/>\n4. constructing triangles<br \/>\n5. constructing quadrilaterals<br \/>\n6. complementary angles<br \/>\n7. supplementary angles<br \/>\n8. vertical angles<\/p>\n<p>Answer:<br \/>\n1. area of a circle = \u03c0 r \u00b2<br \/>\n2. semicircle = ( \u03c0\u00a0 +\u00a0 r \u00b2\/2)<br \/>\n3. composite figure = The figure that consists of two or more geometric shapes.<br \/>\n4. constructing triangles = A triangle is a 3 &#8211; sided polygon made up of three sides having 3 angles.<br \/>\n5. constructing quadrilateral = quadrilateral can be categorized by the lengths of its sides and the size of its angles.<br \/>\n6. complementary angles = Two angles are called complimentary when their measures add to 90\u00b0<br \/>\n7. supplementary angles = two angles are called supplementary when their measures add to 180\u00b0<br \/>\n8. vertical angles = The angles opposite each other when two lines cross.<\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-4.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 4\" width=\"598\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-4.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-4-300x40.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p><strong>9.1 Circles and Circumference (pp. 361\u2013368)<\/strong><br \/>\nLearning Target: Find the circumference of a circle.<\/p>\n<p>Question 1.<br \/>\nWhat is the radius of a circular lid with a diameter of 5 centimeters?<br \/>\nAnswer:<br \/>\nradius = 50 mm<\/p>\n<p>Explanation:<br \/>\nradius\u00a0 = ( d \/ 2)<br \/>\nradius\u00a0 = (5\/ 2) cm<br \/>\nr = 2.5\u00a0 cm<\/p>\n<p>Question 2.<br \/>\nThe radius of a circle is 25 millimeters. Find the diameter.<br \/>\nAnswer:<br \/>\nDiameter = 50 mm<\/p>\n<p>Explanation:<br \/>\ndiameter = 2 x radius<br \/>\ndiameter = 2 x 25\u00a0 mm<br \/>\nd = 50 mm<\/p>\n<p><strong>Find the circumference of the object. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-5.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 5\" width=\"144\" height=\"115\" \/><br \/>\nAnswer:<br \/>\ncircumference of the object = 37.68 sq mm<\/p>\n<p>Explanation:<br \/>\nD. circumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 6 where r =6 given<br \/>\ncircle = 6.28 x\u00a0 6<br \/>\ncircle =37.68 sq mm<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-6.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 6\" width=\"140\" height=\"110\" \/><br \/>\nAnswer:<br \/>\ncircumference of the object = 4.71 sq ft<\/p>\n<p>Explanation:<br \/>\nD. circumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 0.75 where r =0.75 given<br \/>\ncircle = 6.28 x\u00a0 0.75<br \/>\ncircle =4.71 sq ft<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-7.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 7\" width=\"155\" height=\"116\" \/><br \/>\nAnswer:<br \/>\ncircumference of the object = 4.71 sq cm<\/p>\n<p>Explanation:<br \/>\nD. circumference of the circle =2\u03c0r<br \/>\ncircle = 2 x 3.14 x 3 .5 where r =3.5 given<br \/>\ncircle = 6.28 x\u00a0 3.5<br \/>\ncircle =21.98\u00a0 sq cm<\/p>\n<p>Question 6.<br \/>\nYou are placing non-slip tape along the perimeter of the bottom of a semicircle-shaped doormat. How much tape will you save applying the tape to the perimeter of the inside semicircle of the doormat? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-8.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 8\" width=\"224\" height=\"117\" \/><br \/>\nAnswer:<br \/>\nthe tape saved = 47 .4 sq in<br \/>\nExplanation:<br \/>\nperimeter of the semicircle = ( \u03c0 + 2 ) r<br \/>\np = ( 3.14 + 2) 15<br \/>\np = (3 .16 ) 15<br \/>\np = 47.4 sq in<\/p>\n<p>Question 7.<br \/>\nYou need to carry a circular cake through a 32-inch wide doorway without tilting it. The circumference of the cake is 100 inches. Will the cake fit through the doorway? Explain.<br \/>\nAnswer:<br \/>\nyes the cake fit through the doorway.<br \/>\nExplanation:<br \/>\nradius of the circle = (c\/2\u03c0)<br \/>\nr= (100\/6.28)<br \/>\nr = 15.923 sq in<\/p>\n<p>Question 8.<br \/>\nEstimate the radius of the Big Ben clock face in London.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-9.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 9\" width=\"220\" height=\"186\" \/><br \/>\nAnswer:<br \/>\nRadius of the Big Ben clock = 7.0063 m<\/p>\n<p>Explanation:<br \/>\nradius of the circle = (c\/2\u03c0)<br \/>\nr= (44\/6.28)<br \/>\nr = 7.0063 m<\/p>\n<p>Question 9.<br \/>\nDescribe and solve a real-life problem that involves finding the circumference of a circle.<br \/>\nAnswer:<br \/>\nThe circumference of a circle = 2 \u03c0 r<\/p>\n<p>Explanation:<br \/>\ncircle = 2 \u03c0 r<br \/>\nwhere r = radius , \u03c0 = 3.14<\/p>\n<p><strong>9.2 Areas of Circles (pp. 369-374)<\/strong><br \/>\nLearning Target: Find the area of a circle.<\/p>\n<p>Find the area of the circle. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-10.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 10\" width=\"110\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nThe area of the circle = 50.24 sq in<\/p>\n<p>Explanation:<br \/>\nArea of the circle = \u03c0 x r x r<br \/>\narea = 3.14 x 4 x 4<br \/>\narea = 3.14 x 16<br \/>\narea = 50.24 sq in<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-11.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 11\" width=\"116\" height=\"99\" \/><br \/>\nAnswer:<br \/>\nThe area of the circle = 379.94 sq cm<\/p>\n<p>Explanation:<br \/>\nArea of the circle = \u03c0 x r x r<br \/>\narea = 3.14 x 11 x 11<br \/>\narea = 3.14 x 121<br \/>\narea = 379.94 sq cm<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-12.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 12\" width=\"110\" height=\"112\" \/><br \/>\nAnswer:<br \/>\nThe area of the circle = 1384.74 sq mm<\/p>\n<p>Explanation:<br \/>\nArea of the circle = \u03c0 x r x r<br \/>\narea = 3.14 x 21 x 21<br \/>\narea = 3.14 x 441<br \/>\narea = 1384.74 sq mm<\/p>\n<p>Question 13.<br \/>\nA desktop is shaped like a semicircle with a diameter of 28 inches. What is the area of the desktop?<br \/>\nAnswer:<br \/>\nThe area of the desktop = 615.44 sq in<\/p>\n<p>Explanation:<br \/>\nArea of the desktop = \u03c0 x r x r<br \/>\narea = 3.14 x 14 x 14<br \/>\narea = 3.14 x 196<br \/>\narea = 615.44 sq in<\/p>\n<p>Question 14.<br \/>\nAn ecologist is studying an algal bloom that has formed on the entire surface of a circular pond. What is the area of the surface of the pond covered by the algal bloom?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-14.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 14\" width=\"281\" height=\"199\" \/><br \/>\nAnswer:<br \/>\nThe area of the surface of the pond covered by the algol bloom = 615.44 ft<\/p>\n<p>Explanation:<br \/>\nArea of the pond = \u03c0 x r x r<br \/>\narea = 3.14 x 14 x 14<br \/>\narea = 3.14 x 196<br \/>\narea = 615.44 sq ft<\/p>\n<p>Question 15.<br \/>\nA knitted pot holder is shaped like a circle. Its radius is 3.5 inches. What is its area?<br \/>\nAnswer:<br \/>\nThe area of the pot holder = 38.465 sq in<\/p>\n<p>Explanation:<br \/>\nArea of the pot holder = \u03c0 x r x r<br \/>\narea = 3.14 x 3.5 x 3.5<br \/>\narea = 3.14 x 12.25<br \/>\narea = 38.465 sq in<\/p>\n<p><strong>9.3 Perimeters and Areas of Composite Figures (pp. 375\u2013380)<\/strong><br \/>\nLearning Target: Find perimeters and areas of composite figures.<\/p>\n<p>Find the perimeter and the area of the figure.<br \/>\nQuestion 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-16.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 16\" width=\"156\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nArea of semicircle = 1.695 sq in<br \/>\nperimeter of semicircle = 15.8 sq in<\/p>\n<p>Explanation:<br \/>\narea of the semicircle = ( \u03c0 + r x r \/2)<br \/>\ns . c = (3.14 + 5 x 5 \/2)<br \/>\ns. c = (3.14 + 25\/2)<br \/>\ns . c = (3.39 \/2 )<br \/>\ns. c = 1.695 sq in<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) x r<br \/>\np= 3.14 + 2 x 5<br \/>\np = 3.16 x 5<br \/>\np = 15.8 sq in<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-17.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 17\" width=\"154\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nArea of semicircle = 6.07 sq ft<br \/>\nperimeter of semicircle = 9.48 sqft<\/p>\n<p>Explanation:<br \/>\narea of the semicircle = ( \u03c0 + r x r \/2)<br \/>\ns . c = (3.14 + 3 x 3 \/2)<br \/>\ns. c = (3.14 + 9\/2)<br \/>\ns . c = (12.14 \/2 )<br \/>\ns. c = 6.07 sq ft<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) x r<br \/>\np= 3.14 + 2 x 3<br \/>\np = 3.16 x 3<br \/>\np = 9.48 sq ft<\/p>\n<p>Question 18.<br \/>\n<strong>GARDEN<\/strong><br \/>\nYou want to fence part of a yard to make a vegetable garden. How many feet of fencing do you need to surround the garden?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-18.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 18\" width=\"214\" height=\"149\" \/><br \/>\nAnswer:<br \/>\nThe fencing need to surround the garden = 32 sq feet<\/p>\n<p>Explanation:<br \/>\narea\u00a0 of the rectangle = l + b<br \/>\narea = 18 + 14<br \/>\narea = 32 sq feet<\/p>\n<p><strong style=\"font-size: 16px;\">9.4 Constructing Polygons (pp. 381-388)<\/strong><\/p>\n<p>Learning Target: Construct a polygon with given measures.<\/p>\n<p>Draw a triangle with the given description, if possible.<br \/>\nQuestion 19.<br \/>\na triangle with angle measures of 15\u00b0, 75\u00b0, and 90\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34635\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-39-300x214.png\" alt=\"\" width=\"300\" height=\"214\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-39-300x214.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-39.png 340w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven triangle with angle measures.<\/p>\n<p>Question 20.<br \/>\na triangle with a 3-inch side and a 4-inch side that meet at a 30\u00b0 angle<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34636\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-40.png\" alt=\"\" width=\"257\" height=\"149\" \/><\/p>\n<p>Question 21.<br \/>\na triangle with side lengths of 5 centimeters, 8 centimeters, and 2 centimeters<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34637\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-41.png\" alt=\"\" width=\"295\" height=\"153\" \/><\/p>\n<p><strong>Draw a quadrilateral with the given angle measures, if possible.<\/strong><br \/>\nQuestion 22.<br \/>\n110\u00b0, 80\u00b0, 70\u00b0, 100\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34638\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-42.png\" alt=\"\" width=\"298\" height=\"180\" \/><\/p>\n<p>Question 23.<br \/>\n105\u00b0, 15\u00b0, 20\u00b0, 40\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34639\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-43-300x202.png\" alt=\"\" width=\"300\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-43-300x202.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-43.png 458w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>9.5 Finding Unknown Angle Measures (pp. 389\u2013396)<\/strong><br \/>\nLearning Target: Use facts about angle relationships to find unknown angle measures.<\/p>\n<p>Use the figure shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-24.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 24\" width=\"172\" height=\"120\" \/><br \/>\nQuestion 24.<br \/>\nName a pair of adjacent angles.<br \/>\nAnswer:<br \/>\nx , y , v , w .<\/p>\n<p>Explanation:<br \/>\nIn the above-given figure, the adjacent angles are x, y, v, w.<\/p>\n<p>Question 25.<br \/>\nName a pair of complementary angles.<br \/>\nAnswer:<br \/>\nu and z<\/p>\n<p>Explanation:<br \/>\ncomplementary angles = u , z<\/p>\n<p>Question 26.<br \/>\nName a pair of supplementary angles.<br \/>\nAnswer:<br \/>\nx , y , v , z<\/p>\n<p>Explanation:<br \/>\nsupplementary are x , y , v , z<br \/>\nQuestion 27.<br \/>\nName a pair of vertical angles.<br \/>\nAnswer:<br \/>\nx , y , v, w<\/p>\n<p>Explanation:<br \/>\npair of vertical angles are x , y , v , w<\/p>\n<p>Classify the pair of angles. Then find the value of x.<br \/>\nQuestion 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-28.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 28\" width=\"113\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nx = 111 degrees.<\/p>\n<p>Explanation :<br \/>\nx = 56<br \/>\nx =180\u00a0 &#8211; 69<br \/>\nx = 111 degree<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-29.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 29\" width=\"141\" height=\"117\" \/><br \/>\nAnswer:<br \/>\nx = 81 degrees.<\/p>\n<p>Explanation :<br \/>\nx + 3\u00a0 = 84<br \/>\nx =84\u00a0 \u00a0&#8211; 3<br \/>\nx = 81\u00a0 degree<\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-30.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 30\" width=\"190\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nx = 3.33degrees.<\/p>\n<p>Explanation :<br \/>\n(4x + 10) = x<br \/>\n10 = x &#8211; 4 x<br \/>\n3 x = 10<br \/>\nx = 3.33\u00a0 degree<\/p>\n<p>Question 31.<br \/>\nDescribe two ways to find the measure of \u22202.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-9-Geometric-Shapes-and-Angles-cr-31.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 9 Geometric Shapes and Angles cr 31\" width=\"178\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nangle 2 = 65<\/p>\n<p>Explanation:<br \/>\nx = 180 &#8211; 115<br \/>\nx = 65<br \/>\n2 = 65<\/p>\n<p>Question 32.<br \/>\nUsing the diagram from Exercises 24\u201327, find all the angle measures when \u2220XUY = 40\u00b0.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Geometric_Shapes_and_Angles_Practice_Test\"><\/a>Geometric Shapes and Angles Practice Test<\/h3>\n<p>Question 1.<br \/>\nFind the radius of a circle with a diameter of 17 inches.<br \/>\nAnswer:<br \/>\nradius of a circle = 8.5 in<\/p>\n<p>Explanation:<br \/>\nradius of a circle = (d \/ 2)<br \/>\nradius =( 17 \/ 2)<br \/>\nradius = 8.5 in<br \/>\nFind (a) the circumference and (b) the area of the circle. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<br \/>\nQuestion 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-pt-2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles pt 2\" width=\"111\" height=\"112\" \/><br \/>\nAnswer:<br \/>\nArea of the circle = 3.14 m<br \/>\ncircumference of the circle = 6.28 m<\/p>\n<p>Explanation:<br \/>\nArea of the circle = \u03c0 x r x r<br \/>\narea = 3.14 x 1 x 1<br \/>\narea = 3.14 m<br \/>\ncircumference of the circle = 2 x \u03c0 x r<br \/>\nc = 2 x 3.14 x 1<br \/>\nc = 6.28 m<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-pt-3.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles pt 3\" width=\"101\" height=\"109\" \/><br \/>\nAnswer:<br \/>\nArea of the circle = 3846.5 sq in<br \/>\ncircumference of the circle = 219. 8 sq in<\/p>\n<p>Explanation:<br \/>\nArea of the circle = \u03c0 x r x r<br \/>\narea = 3.14 x 35 x 35<br \/>\narea = 3.14 x 1,225 sq in<br \/>\narea = 3846.5 sq in<br \/>\ncircumference of the circle = 2 x \u03c0 x r<br \/>\nc = 2 x 3.14 x 35<br \/>\nc = 6.28 x 35<br \/>\nc = 219.8 sq in<\/p>\n<p>Find (a) the perimeter and (b) the area of the figure. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-pt-4.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles pt 4\" width=\"170\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nArea of semicircle = 2.695 sq ft<br \/>\nperimeter of semicircle = 4. 74 sq ft<\/p>\n<p>Explanation:<br \/>\narea of the semicircle = ( \u03c0 + r x r \/2)<br \/>\ns . c = (3.14 + 1.5 x 1.5 \/2)<br \/>\ns. c = (3.14 + 2.25 \/2)<br \/>\ns . c = (5.39 \/2 )<br \/>\ns. c = 2.695 sq ft<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) x r<br \/>\np= 3.14 + 2 x 1.5<br \/>\np = 3.16 x 1.5<br \/>\np = 4. 74 sq ft<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-pt-5.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles pt 5\" width=\"194\" height=\"131\" \/><br \/>\nAnswer:<br \/>\nArea of semicircle = 9.57 sq ft<br \/>\nperimeter of semicircle = 12.64 sq ft<\/p>\n<p>Explanation:<br \/>\narea of the semicircle = ( \u03c0 + r x r \/2)<br \/>\ns . c = (3.14 + 4 x 4 \/2)<br \/>\ns. c = (3.14 + 16 \/2)<br \/>\ns . c = (19.14 \/2 )<br \/>\ns. c = 9.57\u00a0 sq ft<br \/>\nperimeter of the semicircle = (\u03c0 + 2 ) x r<br \/>\np= 3.14 + 2 x 4<br \/>\np = 3.16 x 4<br \/>\np = 12.64 sq ft<\/p>\n<p><strong>Draw a figure with the given description, if possible.<\/strong><br \/>\nQuestion 6.<br \/>\na triangle with sides of length 5 inches and 6 inches that meet at a 50\u00b0 angle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34641\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-44.png\" alt=\"\" width=\"252\" height=\"194\" \/><\/p>\n<p>Question 7.<br \/>\na triangle with side lengths of 3 inches, 4 inches, and 5 inches<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-34643\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-45.png\" alt=\"\" width=\"265\" height=\"224\" \/><\/p>\n<p>Question 8.<br \/>\na quadrilateral with angle measures of 90\u00b0, 110\u00b0, 40\u00b0, and 120\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-46-300x165.png\" alt=\"\" width=\"300\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-46-300x165.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-46.png 325w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Classify each pair of angles. Then find the value of x.<\/strong><br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-pt-9.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles pt 9\" width=\"133\" height=\"79\" \/><br \/>\nAnswer:<br \/>\nx = 9 degrees.<\/p>\n<p>Explanation:<br \/>\n(8x + 2) = 74<br \/>\n8x = 74 &#8211; 2<br \/>\n8x = 72<br \/>\nx = (72\/8)<br \/>\nx = 9<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-pt-10.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles pt 10\" width=\"115\" height=\"88\" \/><br \/>\nAnswer:<br \/>\nx = 50 degrees.<\/p>\n<p>Explanation:<br \/>\n(x + 6) = 56<br \/>\nx = 56 &#8211; 6<br \/>\nx = 50<br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-pt-11.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles pt 11\" width=\"171\" height=\"87\" \/><br \/>\nAnswer:<br \/>\nx = 67 degrees.<\/p>\n<p>Explanation:<br \/>\nx = 180 &#8211; 113<br \/>\nx = 67 degrees.<\/p>\n<p>Question 12.<br \/>\nA museum plans to rope off the perimeter of the 60 ftL-shaped exhibit. How much rope does it need?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-pt-12.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles pt 12\" width=\"209\" height=\"141\" \/><br \/>\nAnswer:<br \/>\nArea of the museum = 2,826 sq ft<\/p>\n<p>Explanation:<br \/>\nArea of the museum\u00a0 = \u03c0 x r x r<br \/>\narea = 3.14 x 30 x 30<br \/>\narea = 3.14 x 900<br \/>\narea =\u00a0 2,826 sq ft<\/p>\n<h3><a id=\"Geometric_Shapes_and_Angles_Cumulative_Practice\"><\/a>Geometric Shapes and Angles Cumulative Practice<\/h3>\n<p>Question 13.<br \/>\nDraw a pair of adjacent angles that are neither complementary nor supplementary.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34645\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-47-300x131.png\" alt=\"\" width=\"300\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-47-300x131.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Geometry-47.png 345w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 14.<br \/>\nThe circumference of a circle is 36.2 centimeters. What is the length of the diameter of the circle?<br \/>\nAnswer:<br \/>\nDiameter of the circle = 11.52866 cm<\/p>\n<p>Explanation:<br \/>\nDiameter of the circle = 2 x r<br \/>\nradius of the circle = (c \/ 2 \u03c0 )<br \/>\ncircumference = 36.2 cm<br \/>\nradius = (36.2 \/ 6.28)<br \/>\nradius = 5.7643<br \/>\ndaimeter = 2 x r<br \/>\ndiameter = 5.7643 x 2<br \/>\ndiameter = 11.52866 cm<\/p>\n<p>Question 15.<br \/>\nThe circular rug is placed on a square floor. The rug touches all four walls. How much of the floor space is not covered by the rug?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-pt-15.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles pt 15\" width=\"125\" height=\"135\" \/><br \/>\nAnswer:<br \/>\nArea of the circle = 176.625sq ft<\/p>\n<p>Explanation:<br \/>\nArea of the circle\u00a0 = \u03c0 x r x r<br \/>\narea = 3.14 x 7.5 x 7.5<br \/>\narea = 3.14 x 56.25<br \/>\narea =\u00a0 176.625 sq ft<\/p>\n<h3>Geometric Shapes and Angles Cumulative Practice<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-28038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles cp 1\" width=\"315\" height=\"349\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-1.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-1-271x300.png 271w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\nQuestion 1.<br \/>\nTo make 6 servings of soup, you need 5 cup of chicken broth. You want to know how many servings you can make with 2 quarts of chicken broth. Which proportion should you use?<br \/>\nA. \\(\\frac{6}{5}=\\frac{2}{x}\\)<br \/>\nB. \\(\\frac{6}{5}=\\frac{x}{2}\\)<br \/>\nC. \\(\\frac{6}{5}=\\frac{x}{8}\\)<br \/>\nD. \\(\\frac{5}{6}=\\frac{x}{8}\\)<br \/>\nAnswer:<br \/>\noption B is correct.<\/p>\n<p>Explanation:<br \/>\nGiven that in the question to make 6 servings of soup you need 5 cup of chicken broth.<\/p>\n<p>Question 2.<br \/>\nWhat is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles cp 2\" width=\"263\" height=\"148\" \/><br \/>\nAnswer:<br \/>\nx = 42 degrees.<\/p>\n<p>Explanation:<br \/>\n(2x + 1) = 85<br \/>\n2x = 85 &#8211; 1<br \/>\n2x = 84<br \/>\nx = (84\/2)<br \/>\nx = 42<\/p>\n<p>Question 3.<br \/>\nYour mathematics teacher described an inequality in words.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-3.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles cp 3\" width=\"263\" height=\"61\" \/><br \/>\nWhich inequality matches your mathematics teacher\u2019s description?<br \/>\nF. 7n &#8211; 5 &lt; 42 G. (7 &#8211; 5)n &gt; 42<br \/>\nH. 5 &#8211; 7n &gt; 42<br \/>\nI. 7n &#8211; 5 &gt; 42<br \/>\nAnswer:<br \/>\noption G is correct.<\/p>\n<p>Explanation:<br \/>\n5 is less than the product of 7 and an unknown number is greater than 42.<br \/>\n(7 &#8211; 5)n &gt; 42<\/p>\n<p>Question 4.<br \/>\nWhat is the approximate area of the circle below? (Use \\(\\frac{22}{7}\\) for \u03c0).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-4.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles cp 4\" width=\"114\" height=\"103\" \/><br \/>\nA. 132 cm<sup>2<\/sup><br \/>\nB. 264 cm<sup>2<\/sup><br \/>\nC. 5544 cm<sup>2<\/sup><br \/>\nD. 22,176 cm<sup>2<\/sup><br \/>\nAnswer:<br \/>\nArea of the circle = 63.585 sq ft<\/p>\n<p>Explanation:<br \/>\nArea of the circle\u00a0 = \u03c0 x r x r<br \/>\narea = 3.14 x 42 x 42<br \/>\narea = 3.14 x 1,764<br \/>\narea =\u00a0 5,538.96 cm<\/p>\n<p>Question 5.<br \/>\nYou have a 50% chance of selecting a blue marble from Bag A and a 20% chance of selecting a blue marble from Bag B. Use the provided simulation to answer the question, \u201cWhat is the estimated probability of selecting a blue marble from both bags?\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-5.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles cp 5\" width=\"439\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-5.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-5-300x160.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><br \/>\nF. 12%<br \/>\nG. 16%<br \/>\nH. 24%<br \/>\nI. 88%<br \/>\nAnswer:<br \/>\noption F is correct.<\/p>\n<p>Explanation:<br \/>\nThe digits 1 and 2 in the ones place represent selecting a blue marble from bag B.<br \/>\nThe digits 1 through 5\u00a0 in the tens place represent selecting a blue marble from bag A.<\/p>\n<p>Question 6.<br \/>\nWhich proportion represents the problem?<br \/>\n\u201cWhat number is 12% of 125?\u201d<br \/>\nA. \\(\\frac{n}{125}=\\frac{12}{100}\\)<br \/>\nB. \\(\\frac{12}{125}=\\frac{n}{100}\\)<br \/>\nC. \\(\\frac{125}{n}=\\frac{12}{100}\\)<br \/>\nD. \\(\\frac{12}{n}=\\frac{125}{100}\\)<br \/>\nAnswer:<br \/>\noption B is correct.<\/p>\n<p>Explanation:<br \/>\n(12\/125 ) x 100<br \/>\n(12\/5) x 4<br \/>\nQuestion 7.<br \/>\nWhat is the approximate perimeter of the figure below? (Use 3.14 for \u03c0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-7.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles cp 7\" width=\"382\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-7.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-7-300x106.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><br \/>\nAnswer:<br \/>\nThe perimeter of the semicircle = 18. 84<\/p>\n<p>Explnation:<br \/>\nperimeter = ( \u03c0 + 2 x r)<br \/>\nperimeter = (6.28 x 3 )<br \/>\nperimeter = 18 . 84<\/p>\n<p>Question 8.<br \/>\nA savings account earns 2.5% simple interest per year. The principal is $850. What is the balance after 3 years?<br \/>\nF. $63.75<br \/>\nG. $871.25<br \/>\nH. $913.75<br \/>\nJ. $7225<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nTwo ponds each contain about 400 fish. The double box-and-whisker plot represents the weights of a random sample of 12 fish from each pond. Which statement about the measures of center and variation is true?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-9.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles cp 9\" width=\"446\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-9.png 446w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-9-300x73.png 300w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><br \/>\nA. The variation in the samples is about the same, but the sample from Pond A has a greater median.<br \/>\nB. The variation in the samples is about the same, but the sample from Pond B has a greater median.<br \/>\nC. The measures of center and variation are about the same for both samples.<br \/>\nD. Neither the measures of center nor variation are the same for the samples.<br \/>\nAnswer:<br \/>\noption D is correct.<\/p>\n<p>Explanation:<br \/>\nNeither the measures of center nor variation are same for the samples.<\/p>\n<p>Question 10.<br \/>\nA lawn sprinkler sprays water onto part of a circular region, as shown below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-28049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-11.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles cp 11\" width=\"363\" height=\"148\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-11.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles-cp-11-300x122.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><br \/>\nPart A What is the area, in square feet, of the region that the sprinkler sprays with water? Explain your reasoning. (Use 3.14 for \u03c0.)<br \/>\nPart B What is the perimeter, in feet, of the region that the sprinkler sprays with water? Explain your reasoning. (Use 3.14 for \u03c0.)<br \/>\nAnswer:<br \/>\npart A The region that sprinkler sprays with water = 1,256 ft<br \/>\npart B The region that sprinkler sprays with water = 125 .6 ft<\/p>\n<p>Explanation:<br \/>\narea of the circle = \u03c0 x r x r<br \/>\narea = 3.14 x 20 x 20<br \/>\narea = 1256 ft<br \/>\nperimeter of the circle =\u00a0 2 x \u03c0 x r<br \/>\nperimeter = 2 x 3.14 x 20<br \/>\nperimeter = 125. 6 ft<\/p>\n<p>Question 11.<br \/>\nWhat is the least value of x for which x &#8211; 12 \u2265 &#8211; 8 is true?<br \/>\nF. &#8211; 20<br \/>\nG. &#8211; 4<br \/>\nH. 4<br \/>\nI. 5<br \/>\nAnswer:<br \/>\noption F is correct.<\/p>\n<p>Explanation:<br \/>\nx &#8211; 12 \u2265 &#8211; 8<br \/>\nx = -20<\/p>\n<p><em>Final Words:<\/em><\/p>\n<p>Access Big Ideas Math Book 7th Grade Answer Key 9 Geometric Shapes and Angles from the direct links presented above. Hit the direct links and prepare yourself for the exam. With the help of the problems, you can test yourself and your capability of solving the problems. Cumulative practice, Chapter review, the Practice test will help you throughout your preparation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Get Big Ideas Math Answer Key for Grade 7 Chapter 9 Geometric Shapes and Angles Pdf here. We are providing free download links to all problems in the upcoming sections. You can understand the concept easily as we are explaining the concept with so many real-time examples. Candidates can improve their problem-solving skills and analytical &#8230; <a title=\"Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7-chapter-9\/\" aria-label=\"More on Big Ideas Math Answers Grade 7 Chapter 9 Geometric Shapes and Angles\">Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":89754,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/04\/Big-Ideas-Math-Answers-Grade-7-Chapter-9-Geometric-Shapes-and-Angles.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/27850"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=27850"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/27850\/revisions"}],"predecessor-version":[{"id":90237,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/27850\/revisions\/90237"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89754"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=27850"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=27850"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=27850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}