{"id":31930,"date":"2022-04-02T16:08:19","date_gmt":"2022-04-02T10:38:19","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=31930"},"modified":"2022-04-07T11:37:37","modified_gmt":"2022-04-07T06:07:37","slug":"big-ideas-math-answers-grade-8-chapter-3","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-3\/","title":{"rendered":"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles"},"content":{"rendered":"<p>Middle School Students who are struggling with the concepts of Big Ideas Math Grade 8 Ch 3 Angles and Triangles need not worry anymore. Big Ideas Math Book 8th Grade Chapter 3 Angles and Triangles help you finish your homework in time and gives you assistance whenever you need it. Detailed Solutions provided in <strong>Big Ideas Math Grade 8 Answers<\/strong> Chapter 3 make it easy for you to attain knowledge regarding the particular topic in a matter of seconds. Access the BIM Book Grade 8 Ch 3 Angles and Triangles Answer Key via direct links and prepare effectively.<\/p>\n<h2>Big Ideas Math Book 8th Grade Answer Key Chapter 3 Angles and Triangles<\/h2>\n<p>Access the Big Ideas Math Grade 8 Ch 3 Angles and Triangles Answers includes questions from the Lessons, Chapter Tests, Assessment Tests, Cumulative Practice, etc. Kick start your preparation and attempt the exam with confidence and stand out from the rest of the crowd. Refer to the direct links available for Grade 8 BIM Book Chapter 3 Angles and Triangles Solution Key and prepare the respective topic accordingly in no time.<\/p>\n<p><strong>Performance<\/strong><\/p>\n<ul>\n<li><a href=\"#Angles_and_Triangles_STEAM_Video\/Performance\">Angles and Triangles STEAM Video\/Performance<\/a><\/li>\n<li><a href=\"#Angles_and_Triangles_Getting_Ready_for_Chapter_3\">Angles and Triangles Getting Ready for Chapter 3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Parallel Lines and Transversals<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.1_Parallel_Lines_and_Transversals\">Lesson 3.1 Parallel Lines and Transversals<\/a><\/li>\n<li><a href=\"#Parallel_Lines_and_Transversals_Homework_&amp;_Practice_3.1\">Parallel Lines and Transversals Homework &amp; Practice 3.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Angles of Triangles<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.2_Angles_of_Triangles\">Lesson 3.2 Angles of Triangles<\/a><\/li>\n<li><a href=\"#Angles_of_Triangles_Homework_&amp;_Practice_3.2\">Angles of Triangles Homework &amp; Practice 3.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Angles of Polygons<\/strong><\/p>\n<ul>\n<li><a href=\"# Lesson_3.3_Angles_of_Polygons\">Lesson 3.3 Angles of Polygons<\/a><\/li>\n<li><a href=\"# Angles_of_Polygons_Homework_&amp;_Practice_3.3\">Angles of Polygons Homework &amp; Practice 3.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Using Similar Triangles<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_3.4_Using_Similar_Triangles\">Lesson 3.4 Using Similar Triangles<\/a><\/li>\n<li><a href=\"#Using_Similar_Triangles_Homework_&amp;_Practice_3.4\">Using Similar Triangles Homework &amp; Practice 3.4<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 3 &#8211; Angles and Triangles<\/strong><\/p>\n<ul>\n<li><a href=\"#Angles_and_Triangles_Connecting_Concepts\">Angles and Triangles Connecting Concepts<\/a><\/li>\n<li><a href=\"#Angles_and_Triangles_Chapter_Review\">Angles and Triangles Chapter Review<\/a><\/li>\n<li><a href=\"#Angles_and_Triangles_Practice_Test\">Angles and Triangles Practice Test<\/a><\/li>\n<li><a href=\"#Angles_and_Triangles_Cumulative_Practice\">Angles and Triangles Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Angles_and_Triangles_STEAM_Video\/Performance\"><\/a>Angles and Triangles STEAM Video\/Performance<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>Each cell in a honeycomb is in the shape of a regular hexagon. Why might bees use this shape?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 1\" width=\"191\" height=\"259\" \/><\/p>\n<p><strong>Watch the STEAM Video \u201cHoneycombs.\u201d Then answer the following questions.<\/strong><\/p>\n<p>Question 1.<br \/>\nEnid and Tony show regular tilings made out of squares, equilateral triangles, and regular hexagons. What is the sum of the interior angle measures of the tiling made from equilateral triangles, outlined below in yellow?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 2\" width=\"407\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-2.png 407w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-2-300x140.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>Answer:<br \/>\nThe sum of interior angles of the equilateral triangle = 180\u00b0<br \/>\nx + x + x = 180\u00b0<br \/>\n3x\u00b0 = 180\u00b0<br \/>\nx = 180\/3<br \/>\nx\u00b0 = 60\u00b0<\/p>\n<p>Question 2.<br \/>\nThe cells in a honeycomb use a tiling pattern of the regular hexagon shown. A cell is 10 millimeters deep. About how much honey can one cell hold? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 3\" width=\"102\" height=\"112\" \/><\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Turtle Shells<\/strong><\/p>\n<p>After 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 angle measures of shapes seen on a turtle shell.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 4\" width=\"390\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-4.png 390w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-4-300x162.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 5\" width=\"289\" height=\"368\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-5.png 289w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-5-236x300.png 236w\" sizes=\"(max-width: 289px) 100vw, 289px\" \/><br \/>\nYou will be asked to \ufb01nd angle sums and missing angle measures. What other animals have features that resemble geometric shapes?<\/p>\n<h3><a id=\"Angles_and_Triangles_Getting_Ready_for_Chapter_3\"><\/a>Angles and Triangles Getting Ready for Chapter 3<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p>When an object is transverse, it is lying or extending across something. In the drawing, the fallen tree lying across the railroad track is transverse to the track.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-6.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 6\" width=\"271\" height=\"142\" \/><br \/>\n<strong>1. Work with a partner.<\/strong><br \/>\n\u2022 Discuss what it means for two lines to be parallel. Decide on a strategy for drawing parallel lines. Then draw two parallel lines.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-7.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 7\" width=\"392\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-7.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-7-300x155.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><br \/>\n\u2022 Draw a third line that intersects the parallel lines. This line is called a transversal<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-8.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 8\" width=\"357\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-8.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-8-300x158.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><br \/>\na. How many angles are formed by the parallel lines and the transversal? Label each angle.<\/p>\n<p>Answer: 8 angles are formed by the parallel lines and the transversal<br \/>\nb. Which of these angles have equal measures? Explain your reasoning.<\/p>\n<p><strong>Vocabulary<\/strong><\/p>\n<p>The following vocabulary terms are de\ufb01ned in this chapter. Think about what the terms might mean and record your thoughts.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-9.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 9\" width=\"473\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-9.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-9-300x36.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<h3><a id=\"Lesson_3.1_Parallel_Lines_and_Transversals\"><\/a>Lesson 3.1 Parallel Lines and Transversals<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Work with a partner. Use geometry software and the lines A and B shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-10.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 10\" width=\"266\" height=\"243\" \/><br \/>\na. Are line A and B line parallel? Explain your reasoning.<br \/>\nb. Draw a line that intersects both line A and line B. What do you notice about the measures of the angles that are created?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-11.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 11\" width=\"159\" height=\"206\" \/><br \/>\nc. Rotate line A or line B until the angles created by the intersection of line A and line C are congruent to the angles created by the intersection of line B and line C. What do you notice about line A and line B?<br \/>\nd. Rotate line to create different angle measures. Are the angles that were congruent in part(c) still congruent?<br \/>\ne. Make a conjecture about the measures of the angles created when a line intersects two parallel lines.<\/p>\n<p><strong>3.1 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Use the \ufb01gure to \ufb01nd the measure of the angle. Explain your reasoning<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-12.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 12\" width=\"193\" height=\"127\" \/><\/p>\n<p>Question 1.<br \/>\n\u22201<\/p>\n<p>Answer: 63\u00b0<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54216\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-3-img_1-300x191.png\" alt=\"Big Ideas Math Grade 8 Answers Chapter 3 img_1\" width=\"300\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-3-img_1-300x191.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-3-img_1.png 444w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\u22201 and 63\u00b0 angle are corresponding angles are formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22201 is 63\u00b0<\/p>\n<p>Question 2.<br \/>\n\u22202<\/p>\n<p>Answer: 117\u00b0<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-3-Angles-and-triangles-answer-key-img_2-300x191.png\" alt=\"BIM Grade 8 Chapter 3 Angles and triangles answer key img_2\" width=\"300\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-3-Angles-and-triangles-answer-key-img_2-300x191.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-3-Angles-and-triangles-answer-key-img_2.png 444w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\u22201 and \u22202 are supplementary angle.<br \/>\n\u22201 + \u22202 = 180\u00b0<br \/>\n63\u00b0 + \u22202 = 180\u00b0<br \/>\n\u22202 = 180\u00b0 &#8211; 63\u00b0<br \/>\n\u22202 = 117\u00b0<br \/>\nSo, the measure of \u22202 = 117\u00b0<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 3.<br \/>\nUse the \ufb01gureto \ufb01nd the measures of the numbered angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-13.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 13\" width=\"226\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and 59\u00b0 are the supplementary angles<br \/>\n\u22201 + 59\u00b0 = 180\u00b0<br \/>\n\u22201 = 180\u00b0 &#8211; 59\u00b0<br \/>\n\u22201 = 121\u00b0<br \/>\n\u22202 and 59\u00b0 are vertical angles. They are congruent.<br \/>\nSo, the measure of \u22201 is 121\u00b0<br \/>\n\u22203 and 59\u00b0 are supplementary angles.<br \/>\n\u22203 + 59\u00b0 = 180\u00b0<br \/>\n\u22203 = 180\u00b0 &#8211; 59\u00b0<br \/>\n\u22203 = 121\u00b0<br \/>\n\u22204, \u22205, \u22206, \u22207 corresponding angles are congruent because they are formed by a transversal intersecting parallel side.<br \/>\nthe measure of\u00a0 \u22204 is 121\u00b0<br \/>\nthe measure of \u22205 is 59\u00b0<br \/>\nthe measure of\u00a0 \u22206 is 121\u00b0<br \/>\nthe measure of \u22207 is 59\u00b0<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>In Example 3, the measure of \u22204 is 84\u00b0. Find the measure of the angle. Explain your reasoning.<\/strong><\/p>\n<p>Question 4.<br \/>\n\u22203<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-img_3-300x215.png\" alt=\"Bigideas Math Answers Grade 8 Chapter 3 Angles and Triangles img_3\" width=\"300\" height=\"215\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-img_3-300x215.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-img_3.png 388w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe measure of \u22204 is 84\u00b0.<br \/>\n\u22203 and \u22204 are supplementary angles.<br \/>\n\u22203 + \u22204 = 180\u00b0<br \/>\n\u22203 + 84\u00b0 = 180\u00b0<br \/>\n\u22203 = 180\u00b0 &#8211; 84\u00b0<br \/>\n\u22203 = 96\u00b0<\/p>\n<p>Question 5.<br \/>\n\u22205<\/p>\n<p>Answer:<br \/>\n\u22204 and \u22205 are alternate interior angles formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22205 is 84\u00b0<\/p>\n<p>Question 6.<br \/>\n\u22206<\/p>\n<p>Answer:<br \/>\n\u22203 and \u22206 are alternate exterior angles formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22206 is 96\u00b0<\/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>FINDING ANGLE MEASURES<\/strong><br \/>\n<strong>Use the \ufb01gure to \ufb01nd the measures of the numbered angles.<\/strong><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-14.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 14\" width=\"161\" height=\"165\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and 120\u00b0 are the supplementary angles.<br \/>\n\u22201 + 120\u00b0 = 180\u00b0<br \/>\n\u22201 = 180 &#8211; 120<br \/>\n\u22201 = 60\u00b0<br \/>\nThus the measure of \u22201 is 60\u00b0<br \/>\n\u22202 and 120\u00b0 are the vertical angles. They are congruent.<br \/>\nThus the measure of \u22202 is 120\u00b0<br \/>\n\u22203 and 120\u00b0 are the supplementary angles.<br \/>\n\u22203 + 120\u00b0 = 180\u00b0<br \/>\n\u22203 = 180 &#8211; 120<br \/>\n\u22203 = 60\u00b0<br \/>\n\u22204, \u22205, \u22206, \u22207 are corresponding angles are formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nThus the measure of \u22204 is 60\u00b0<br \/>\nThus the measure of \u22205 is 120\u00b0<br \/>\nThus the measure of \u22206 is 120\u00b0<br \/>\nThus the measure of \u22207 is 60\u00b0<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-15.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 15\" width=\"194\" height=\"160\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and 35\u00b0 are the supplementary angles.<br \/>\n\u22201 + 35\u00b0 = 180\u00b0<br \/>\n\u22201 = 180 &#8211; 35<br \/>\n\u22201 = 145\u00b0<br \/>\nThus the measure of \u22201 is 145\u00b0<br \/>\n\u22202 and 35\u00b0 are the supplementary angles.<br \/>\n\u22202 + 35\u00b0 = 180\u00b0<br \/>\n\u22202 = 180 &#8211; 35<br \/>\n\u22202 = 145\u00b0<br \/>\nThus the measure of \u22202 is 145\u00b0<br \/>\n\u22203 and 35\u00b0 are the vertical angles. They are congruent.<br \/>\nThus the measure of \u22203 is 35\u00b0<br \/>\n\u22204, \u22205, \u22206, \u22207 are corresponding angles are formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nThus the measure of \u22204 is 35\u00b0<br \/>\nThus the measure of \u22205 is 145\u00b0<br \/>\nThus the measure of \u22206 is 145\u00b0<br \/>\nThus the measure of \u22207 is 35\u00b0<\/p>\n<p>Question 9.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich angle measure does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-16.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 16\" width=\"616\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-16.png 616w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-16-300x67.png 300w\" sizes=\"(max-width: 616px) 100vw, 616px\" \/><\/p>\n<p>Answer:<br \/>\n\u22202, \u22206 are corresponding angles are formed by transversal intersecting parallel lines.<br \/>\n\u22206, \u22208 are vertical angles are formed by transversal intersecting parallel lines.<br \/>\n\u22205 does not belong to the other three because all the other three measure are equal.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 10.<br \/>\nA cross section of a pier is shown. Find the value of a. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-17.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 17\" width=\"223\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\nThe angle a and the angle of 70 degrees are complementary angles because they belong to a right triangle, where the third angle is the right angle.<br \/>\n\u2220a + 70 = 90<br \/>\n\u2220a = 90 &#8211; 70<br \/>\n\u2220a = 20\u00b0<\/p>\n<p>Question 11.<br \/>\nThe head tube angle of a bike determines how easy the bike is to steer. A bike frame with angle approximations is shown. What is the head tube angle of the bike?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-18.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 18\" width=\"224\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nThe lines AB and CD are parallel.<br \/>\nABC and BCD are the corresponding angles formed by transversal intersecting parallel lines.<br \/>\n\u2220BCD = 55\u00b0<br \/>\n\u2220BAC + \u2220ABC + \u2220ACB = 180\u00b0<br \/>\nThe sum of the angles in a triangle is 180\u00b0<br \/>\n\u2220BAC + 55\u00b0+ 52\u00b0 = 180\u00b0<br \/>\n\u2220BAC + 107\u00b0 = 180\u00b0<br \/>\n\u2220BAC = 180\u00b0 &#8211; 107\u00b0<br \/>\n\u2220BAC = 73\u00b0<br \/>\nSo, the head tube angle of a bike is 73\u00b0<\/p>\n<h3><a id=\"Parallel_Lines_and_Transversals_Homework_&amp;_Practice_3.1\"><\/a>Parallel Lines and Transversals Homework &amp; Practice 3.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the values of the ratios (red to blue) of the perimeters and areas of the similar \ufb01gures.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-19.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 19\" width=\"209\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nperimeter of red hexagon\/perimeter of blue hexagon = \\(\\frac{3}{5}\\)<br \/>\nThe values of the ratios of the perimeter is \\(\\frac{3}{5}\\)<br \/>\nArea of red hexagon\/Area of blue hexagon = (\\(\\frac{3}{5}\\))\u00b2 = \\(\\frac{9}{25}\\)<br \/>\nThe values of the ratios of the area is \\(\\frac{9}{25}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-20.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 20\" width=\"288\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nperimeter of red trapezium \/perimeter of blue trapezium = \\(\\frac{7}{6}\\)<br \/>\nThe values of the ratios of the perimeter is \\(\\frac{7}{6}\\)<br \/>\nArea of red hexagon\/Area of blue hexagon = (\\(\\frac{7}{6}\\))\u00b2 = \\(\\frac{49}{36}\\)<br \/>\nThe values of the ratios of the area is \\(\\frac{49}{36}\\)<\/p>\n<p><strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 3.<br \/>\n4 + 3<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n4 + 9 = 13<\/p>\n<p>Question 4.<br \/>\n5(2)<sup>2<\/sup> &#8211; 6<\/p>\n<p>Answer:<br \/>\n5(4) &#8211; 6<br \/>\n20 &#8211; 6 = 14<\/p>\n<p>Question 5.<br \/>\n11 + (-7)<sup>2<\/sup> &#8211; 9<\/p>\n<p>Answer:<br \/>\n11 + 49 &#8211; 9<br \/>\n11 + 40 = 50<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>EXPLORING INTERSECTIONS OF LINES<\/strong><br \/>\n<strong>Use a protractor to determine whether lines a and b are parallel. (<\/strong>See Exploration 1, p. 103.)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-21.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 21\" width=\"143\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\nUse a protractor to measure \u22201 and \u22202<br \/>\n\u22201 \u2248 60\u00b0<br \/>\n\u22202 \u2248 60\u00b0<br \/>\n\u22201 and \u22202, it means the two angles are congruent. The angles are exterior alternate angles.<br \/>\nAccording to the converse of the exterior alternate angles theorem, the two lines are parallel.<br \/>\na || b<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-22.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 22\" width=\"200\" height=\"166\" \/><\/p>\n<p>Answer:<br \/>\nUse a protractor to measure \u22201 and \u22202<br \/>\n\u22201 \u2248 50\u00b0<br \/>\n\u22202 \u2248 60\u00b0<br \/>\n\u22201 and \u22202, it means the two angles are not congruent. The angles are exterior alternate angles.<br \/>\nAccording to the converse of the exterior alternate angles theorem, the two lines are not parallel.<\/p>\n<p><strong>FINDING ANGLE MEASURES<\/strong><br \/>\n<strong>Use the \ufb01gure to \ufb01nd the measures of the numbered angles. Explain your reasoning.<\/strong><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-23.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 23\" width=\"168\" height=\"133\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and 107\u00b0 are corresponding angles. They are congruent.<br \/>\nSo, the measure of \u22201 is 107\u00b0.<br \/>\n\u22201 and \u22202 are supplementary angles.<br \/>\n\u22201 + \u22202 = 180\u00b0<br \/>\n107\u00b0 + \u22202 = 180\u00b0<br \/>\n\u22202 = 180\u00b0 &#8211; 107\u00b0<br \/>\n\u22202 = 73\u00b0<br \/>\nSo, the measure of \u22202 is 73\u00b0<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-24.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 24\" width=\"162\" height=\"148\" \/><\/p>\n<p>Answer:<br \/>\n\u22203 and 95\u00b0 are corresponding angles. They are congruent.<br \/>\nThus the measure of \u22203 is 95\u00b0<br \/>\n\u22203 and \u22204 are supplementary angles.<br \/>\n\u22203 + \u22204 = 180\u00b0<br \/>\n95\u00b0 + \u22204 = 180\u00b0<br \/>\n\u22204 = 180 &#8211; 95<br \/>\n\u22204 = 85\u00b0<br \/>\nSo the measure of \u22204 is 85\u00b0<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-25.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 25\" width=\"173\" height=\"143\" \/><\/p>\n<p>Answer:<br \/>\n\u22205 and 49\u00b0 are corresponding angles. They are congruent.<br \/>\nSo, the measure of \u22205 is 49\u00b0<br \/>\n\u22205 and \u22206 are supplementary angles.<br \/>\n\u22205 + \u22206 = 180\u00b0<br \/>\n49\u00b0 + \u22206 = 180\u00b0<br \/>\n\u22206 = 180\u00b0 &#8211; 49\u00b0<br \/>\n\u22206 = 131\u00b0<br \/>\nSo, the measure of \u22206 is 131\u00b0<\/p>\n<p>Question 11.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend describes a relationship between the angles shown. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-26.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 26\" width=\"344\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-26.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-26-300x109.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><\/p>\n<p>Answer:<br \/>\nSince the two lines are not parallel. Hence \u22205 is not congruent to \u22206.<br \/>\nBy this, we can say that your friend is not correct.<\/p>\n<p>Question 12.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe painted lines that separate parking spaces are parallel. The measure of \u22201 is 60\u00b0. What is the measure of \u22202? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-27.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 27\" width=\"202\" height=\"224\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and \u22202 are corresponding angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nThe measure of \u22201 is 60\u00b0 so the measure of \u22202 is 60\u00b0<\/p>\n<p>Question 13.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nDescribe two real-life situations that use parallel lines.<\/p>\n<p>Answer:<br \/>\nExample 1: The railroad tracks and the tram tracks are parallel lines.<br \/>\nExample 2:\u00a0 The shelves of a bookcase.<\/p>\n<p><strong>USING CORRESPONDING ANGLES<\/strong><br \/>\n<strong>Use the \ufb01gure to \ufb01nd the measures of the numbered angles.<\/strong><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-28.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 28\" width=\"169\" height=\"145\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and 60\u00b0 are corresponding angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\n\u22201 and \u22202 are supplementary angles.<br \/>\n\u22201 + \u22202 = 180\u00b0<br \/>\n60\u00b0 + \u22202 = 180\u00b0<br \/>\n\u22202 = 180\u00b0 &#8211; 60\u00b0<br \/>\n\u22202 = 119\u00b0<br \/>\nSo, the measure of \u22202 is 119\u00b0<br \/>\n\u22203 and \u22201 are vertical angles. They are congruent.<br \/>\nSo, the measure of \u22203 is 61\u00b0<br \/>\n\u22204 and \u22202 are vertical angles. They are congruent.<br \/>\n\u22205, \u22206, \u22207 corresponding angles are congruent because they are formed by a transversal intersecting parallel lines.<br \/>\nSo, the measure of \u22205 is 119\u00b0<br \/>\nSo, the measure of \u22206 is 61\u00b0<br \/>\nSo, the measure of \u22207 is 119\u00b0<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-29.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 29\" width=\"182\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and 99\u00b0 are supplementary angles.<br \/>\n\u22201 + 99\u00b0 = 180\u00b0<br \/>\n\u22201 = 180\u00b0 &#8211; 99\u00b0<br \/>\n\u22201 = 81\u00b0<br \/>\nThus the measure of \u22201 is 81\u00b0<br \/>\n\u22202 and 99\u00b0 are vertical angles. They are congruent.<br \/>\nThe measure of \u22202 is 99\u00b0<br \/>\n\u22203 and \u22201 are vertical angles. They are congruent.<br \/>\nSo, the measure of \u22203 is 81\u00b0<br \/>\n\u22204, \u22205, \u22206, \u22207 corresponding angles are congruent because they are formed by a transversal intersecting parallel lines.<br \/>\nSo, the measure of \u22204 is 99\u00b0<br \/>\nSo, the measure of \u22205 is 81\u00b0<br \/>\nSo, the measure of \u22206 is 99\u00b0<br \/>\nSo, the measure of \u22207 is 81\u00b0<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-30.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 30\" width=\"169\" height=\"177\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and 90\u00b0 are supplementary angles.<br \/>\n\u22201 + 90\u00b0 = 180\u00b0<br \/>\n\u22201 = 180\u00b0 &#8211; 90\u00b0<br \/>\n\u22201 = 90\u00b0<br \/>\nThus the measure of \u22201 is 90\u00b0<br \/>\n\u22202 and 90\u00b0 are vertical angles. They are congruent.<br \/>\nThus the measure of \u22202 is 90\u00b0<br \/>\n\u22203 and \u22201 are vertical angles. They are congruent.<br \/>\nSo, the measure of \u22203 is 90\u00b0<br \/>\n\u22204, \u22205, \u22206, \u22207 corresponding angles are congruent because they are formed by a transversal intersecting parallel lines.<br \/>\nSo, the measure of \u22204 is 90\u00b0<br \/>\nSo, the measure of \u22205 is 90\u00b0<br \/>\nSo, the measure of \u22206 is 90\u00b0<br \/>\nSo, the measure of \u22207 is 90\u00b0<\/p>\n<p><strong>USING CORRESPONDING ANGLES<\/strong><br \/>\n<strong>Complete the statement. Explain your reasoning.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-30.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 30.1\" width=\"202\" height=\"130\" \/><\/p>\n<p>Question 17.<br \/>\nIf the measure of \u22201 = 124\u00b0, then the measure of <img loading=\"lazy\" class=\"alignnone size-full wp-image-32005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-31.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 31\" width=\"84\" height=\"40\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and \u22208 are corresponding angles. They are congruent.<br \/>\nThe measure of \u22201 = 124\u00b0, then the measure of \u22208 is 124\u00b0<br \/>\n\u22208 and \u22204 are supplementary angles.<br \/>\n\u22208 + \u22204 = 180\u00b0<br \/>\n124\u00b0 + \u22204 = 180\u00b0<br \/>\n\u22204 = 180\u00b0 &#8211; 124\u00b0<br \/>\n\u22204 = 56\u00b0<br \/>\nSo, the measure of \u22204 is 56\u00b0<\/p>\n<p>Question 18.<br \/>\nIf the measure of \u22202 = 48\u00b0, then the measure of <img loading=\"lazy\" class=\"alignnone size-full wp-image-32007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-32.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 32\" width=\"88\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\n\u22202 and \u22207 are corresponding angles. They are congruent.<br \/>\nThe measure of \u22202 = 48\u00b0, then the measure of \u22207 is 48\u00b0<br \/>\n\u22207 and \u22203 are supplementary angles.<br \/>\n\u22207 + \u22203 = 180\u00b0<br \/>\n48\u00b0 + \u22203 = 180\u00b0<br \/>\n\u22203 = 180\u00b0 &#8211; 48\u00b0<br \/>\n\u22203 = 132\u00b0<br \/>\nThus the measure of \u22203 = 132\u00b0<\/p>\n<p>Question 19.<br \/>\nIf the measure of \u22204 = 55\u00b0, then the measure of <img loading=\"lazy\" class=\"alignnone size-full wp-image-32009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-33.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 33\" width=\"83\" height=\"33\" \/><\/p>\n<p>Answer:<br \/>\n\u22204 and \u22202 are alternate interior angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22202 is 55\u00b0<\/p>\n<p>Question 20.<br \/>\nIf the measure of \u22206 = 120\u00b0, then the measure of <img loading=\"lazy\" class=\"alignnone size-full wp-image-32011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-34.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 34\" width=\"90\" height=\"32\" \/><\/p>\n<p>Answer:<br \/>\n\u22206 and \u22208 are alternate exterior angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22208 is 120\u00b0<\/p>\n<p>Question 21.<br \/>\nIf the measure of \u22207 = 50.5\u00b0, then the measure of <img loading=\"lazy\" class=\"alignnone size-full wp-image-32014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-35.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 35\" width=\"85\" height=\"39\" \/><\/p>\n<p>Answer:<br \/>\n\u22207 and \u22202 are corresponding angles. They are congruent.<br \/>\nThe measure of \u22207 is 50.5\u00b0, so the measure of \u22202 is 50.5\u00b0<br \/>\n\u22202 and \u22206 are supplementary angle.<br \/>\n\u22202 + \u22206 = 180\u00b0<br \/>\n50.5\u00b0 + \u22206 = 180\u00b0<br \/>\n\u22206 = 180\u00b0 &#8211; 50.5\u00b0<br \/>\n\u22206 = 129.5\u00b0<br \/>\nSo, the measure of \u22206 is 129.5\u00b0<\/p>\n<p>Question 22.<br \/>\nIf the measure of \u22203 = 118.7\u00b0, then the measure of <img loading=\"lazy\" class=\"alignnone size-full wp-image-32012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-35.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 35.1\" width=\"91\" height=\"36\" \/><\/p>\n<p>Answer:<br \/>\n\u22203 and \u22206 are corresponding angles. They are congruent.<br \/>\nThe measure of \u22203 is 118.7\u00b0<br \/>\nSo, the measure of \u22206 is 118.7\u00b0<br \/>\n\u22206 and \u22202 are supplementary angles.<br \/>\n\u22206 + \u22202 = 180\u00b0<br \/>\n118.7\u00b0 + \u22202 = 180\u00b0<br \/>\n\u22202 = 180\u00b0 &#8211; 118.7\u00b0<br \/>\n\u22202 = 61.3\u00b0<br \/>\nSo, the measure of \u22202 is 61.3\u00b0<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA rainbow forms when sunlight re\ufb02ects of raindrops at different angles. For blue light, the measure \u22202 is 40\u00b0. What is the measure of \u22201?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-31.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 31.1\" width=\"324\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-31.1.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-31.1-300x152.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><\/p>\n<p>Answer:<br \/>\n\u22204 and \u22205 are alternate interior angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22201 is 40\u00b0<\/p>\n<p>Question 24.<br \/>\n<strong>REASONING<\/strong><br \/>\nIs there a relationship between exterior angles that lie on the same side of a transversal? interior angles that lie on the same side of a transversal? Explain.<\/p>\n<p>Answer:<br \/>\n\u22207 and \u22208 are Exterior angles that lie on the same side of the transversal. Hence \u22207 and \u22208 are supplementary angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-grade-8-Chapter-3-Angles-and-Triangles-img_4-300x220.png\" alt=\"Big Ideas Math Answers grade 8 Chapter 3 Angles and Triangles img_4\" width=\"300\" height=\"220\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-grade-8-Chapter-3-Angles-and-Triangles-img_4-300x220.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-grade-8-Chapter-3-Angles-and-Triangles-img_4.png 421w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\u22203 and \u22204 are interior angles that lie on the same side of the transversal. Hence \u22203 and \u22204 are supplementary angles.<\/p>\n<p>Question 25.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhen a transversal is perpendicular to two parallel lines, all the angles formed measure 90\u00b0. Explain why.<\/p>\n<p>Answer:<br \/>\nWhen a transversal is perpendicular to two parallel lines, all the angles formed measure 90\u00b0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54501\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-3-img-300x220.png\" alt=\"Big Ideas Math Grade 8 Answers Chapter 3 img\" width=\"300\" height=\"220\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-3-img-300x220.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-3-img.png 421w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nAll the angles formed are 90 degrees because perpendicular lines form 90 degree angles.<\/p>\n<p>Question 26.<br \/>\n<strong>REASONING<\/strong><br \/>\nTwo horizontal lines are cut by a transversal. What is the least number of angle measures you need to know to \ufb01nd the measure of every angle? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54502\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-3-Angles-and-triangles-answers-img_6-300x220.png\" alt=\"BIM Grade 8 Chapter 3 Angles and triangles answers img_6\" width=\"300\" height=\"220\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-3-Angles-and-triangles-answers-img_6-300x220.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Chapter-3-Angles-and-triangles-answers-img_6.png 421w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nIn the below example two horizontal lines a and b are cut by a transversal line t, we know only one angle 61 the measure of all the angles are find with the help of one known measure, 61\u00b0<br \/>\n\u22201 and 61\u00b0 are corresponding angles formed by a transversal intersecting parallel lines. the angles are congruent.<br \/>\nThus the measure of \u22201 is 61\u00b0<br \/>\n\u22201 and \u22202 are supplementary angles.<br \/>\n\u22201 + \u22202 = 180\u00b0<br \/>\n61\u00b0 + \u22202 = 180\u00b0<br \/>\n\u22202 = 180\u00b0 &#8211; 61\u00b0<br \/>\n\u22202 = 119\u00b0<br \/>\nThus the measure of \u22202 is 119\u00b0<br \/>\n\u22203 and \u22201 are vertical angles. They are congruent.<br \/>\nThus the measure of \u22203 is 61\u00b0<br \/>\n\u22204 and \u22202 are vertical angles. They are congruent.<br \/>\nThus the measure of \u22204 is 119\u00b0<br \/>\n\u22205, \u22206, \u22207 corresponding angles are formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nThus the measure of \u22205 is 119\u00b0<br \/>\nThus the measure of \u22206 is 61\u00b0<br \/>\nThus the measure of \u22207 is 119\u00b0<\/p>\n<p>Question 27.<br \/>\n<strong>LOGIC<\/strong><br \/>\nDescribe two ways you can show that \u22201 is congruent to \u22207.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-32.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 32.1\" width=\"193\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and \u22207 are alternate exterior angles formed by a transeversal intersecting parallel lines. So, \u22201 and \u22207 are congruent.<br \/>\n\u22201 and \u22205 are corresponding angles formed by a transeversal intersecting parallel lines. So, \u22201 and \u22205 are congruent.<br \/>\n\u22205 and \u22207 are vertical angles so they are congruent.<br \/>\nHence \u22201 and \u22207 are congruent.<\/p>\n<p><strong>FINDING A VALUE<\/strong><br \/>\n<strong>Find the value of x.<\/strong><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-33.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 33.1\" width=\"258\" height=\"194\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and 50\u00b0 are alternate interior angles. They are congruent.<br \/>\nSo, the measure of \u22201 is 50\u00b0<br \/>\n\u22202 and \u22201 are corresponding angles. They are congruent.<br \/>\nSo, the measure of \u22202 is 50\u00b0<br \/>\n\u22202 and x are supplementary angle.<br \/>\n\u22202 + x = 180\u00b0<br \/>\n50\u00b0 + x = 180\u00b0<br \/>\nx = 180\u00b0 &#8211; 50\u00b0<br \/>\nx = 130\u00b0<br \/>\nSo, the measure of x is 130\u00b0<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-34.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 34.1\" width=\"269\" height=\"203\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 and 115\u00b0 are corresponding angles. They are congruent.<br \/>\nSo, the measure of \u22201 is 115\u00b0<br \/>\n\u22201 and x are alternate exterior angles. They are congruent.<br \/>\nSo, the measure of x is 115\u00b0<\/p>\n<p>Question 30.<br \/>\n<strong>PROJECT<\/strong><br \/>\nTrace line p and line t on a piece of paper. Label \u22201. Move the paper so that \u22201 aligns with \u22208. Describe the transformations that you used to show that \u22201 is congruent to \u22208.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-35.2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 35.2\" width=\"208\" height=\"147\" \/><\/p>\n<p>Answer: 180\u00b0 rotation, translation about line t.<\/p>\n<p>Question 31.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nRefer to the \ufb01gure.<br \/>\na. Do the horizontal lines appear to be parallel? Explain.<\/p>\n<p>Answer: The three horizontal lines seem to spread apart, even though in reality they are parallel.<\/p>\n<p>b. Draw your own optical illusion using parallel lines.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-36.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 36\" width=\"355\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-36.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-36-300x121.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54506\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solution-Key-Grade-8-Chapter-3-img_7-300x221.png\" alt=\"Big Ideas Math Solution Key Grade 8 Chapter 3 img_7\" width=\"300\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solution-Key-Grade-8-Chapter-3-img_7-300x221.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solution-Key-Grade-8-Chapter-3-img_7.png 378w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe \ufb01gure shows the angles used to make a shot on an air hockey table.<br \/>\na. Find the value of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-37.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 37\" width=\"336\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-37.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-37-300x177.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p>Answer:<br \/>\nAs the lines AB and CD are parallel and \u2220BCD are alternate interior angles transversal BC, they are congruent.<br \/>\n\u2220ABC \u2245 \u2220BCD<br \/>\nx = 64<br \/>\nb. How does the angle the puck hits the edge of the table relate to the angle it leaves the edge of the table?<\/p>\n<p>Answer:<br \/>\nm\u2220MBA + m\u2220ABC + m\u2220CBN = 180\u00b0<br \/>\n58 \u00b0 + 64\u00b0 + m\u2220CBN = 180\u00b0<br \/>\n122 \u00b0 + m\u2220CBN = 180\u00b0<br \/>\nm\u2220CBN = 180\u00b0 &#8211; 122 \u00b0<br \/>\nm\u2220CBN = 58\u00b0<\/p>\n<h3><a id=\"Lesson_3.2_Angles_of_Triangles\"><\/a>Lesson 3.2 Angles of Triangles<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Exploring Interior and Exterior Angles of Triangles<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Draw several triangles using geometry software. What can you conclude about the sums of the angle measures?<br \/>\nb. You can extend one side of a triangle to form an exterior angle as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-38.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 38\" width=\"242\" height=\"100\" \/><br \/>\nUse geometry software to draw a triangle and an exterior angle. Compare the measure of the exterior angle with the measures of the interior angles. Repeat this process for several different triangles. What can you conclude?<\/p>\n<p>Answer:<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Using Parallel Lines and Transversals<\/strong><br \/>\n<strong>Work with a partner. Describe what is shown in the \ufb01gure below. Then use what you know about parallel lines and transversals to justify your conclusions in Exploration 1.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-39.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 39\" width=\"613\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-39.png 613w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-39-300x106.png 300w\" sizes=\"(max-width: 613px) 100vw, 613px\" \/><\/p>\n<p>Answer:<\/p>\n<p><strong>3.2 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the measures of the interior angles of the triangle.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-40.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 40\" width=\"208\" height=\"101\" \/><\/p>\n<p>Answer: 81\u00b0, 25\u00b0, 74\u00b0<\/p>\n<p>Explanation:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + 81\u00b0 + 25\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 81\u00b0 &#8211; 25\u00b0<br \/>\nx = 74\u00b0<br \/>\nThus the measure of the interior angle is 74\u00b0<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-41.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 41\" width=\"166\" height=\"97\" \/><\/p>\n<p>Answer: 43\u00b0, 51\u00b0, 86\u00b0<\/p>\n<p>Explanation:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + (x &#8211; 35)\u00b0 + 43\u00b0 = 180\u00b0<br \/>\nx\u00b0 + x\u00b0 &#8211; 35\u00b0 + 43\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + 8\u00b0 = 180\u00b0<br \/>\n2x\u00b0 = 180\u00b0 &#8211; 8\u00b0<br \/>\n2x\u00b0 = 172\u00b0<br \/>\nx\u00b0 = 172\u00b0\/2<br \/>\nx\u00b0 = 86\u00b0<br \/>\nThe measure of the interior angle of the triangle<br \/>\n(x &#8211; 35)\u00b0 = 86 &#8211; 35<br \/>\n(x &#8211; 35)\u00b0 = 51\u00b0<br \/>\nx\u00b0 = 51\u00b0 + 35\u00b0<br \/>\nx\u00b0 = 86\u00b0<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 4.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow many exterior angles does a triangle have at each vertex? Explain.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54523\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-Chapter-3-img_8-300x270.png\" alt=\"BIM 8th Grade Answers Chapter 3 img_8\" width=\"300\" height=\"270\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-Chapter-3-img_8-300x270.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-Chapter-3-img_8.png 351w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nAt each vertex of a triangle, there are two exterior angles, which are congruent.<\/p>\n<p><strong>FINDING ANGLE MEASURES<\/strong><br \/>\n<strong>Find the value of x.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-42.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 42\" width=\"171\" height=\"89\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + 25\u00b0 + 40\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 65\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 65\u00b0<br \/>\nx\u00b0 = 115\u00b0<br \/>\nThus the value of x is 115\u00b0<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-43.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 43\" width=\"180\" height=\"104\" \/><\/p>\n<p>Answer:<br \/>\nx\u00b0 = 50\u00b0 + 55\u00b0<br \/>\nx\u00b0 = 105\u00b0<br \/>\nThus the value of x is 105\u00b0<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\nThe Historic Triangle in Virginia connects Jamestown, Williamsburg, and Yorktown. The interior angle at Williamsburg is 120\u00b0. The interior angle at Jamestown is twice the measure of the interior angle at Yorktown. Find the measures of the interior angles at Jamestown and Yorktown. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nThe interior angle at Williamsburg is 120\u00b0.<br \/>\nLet the interior angles at Jamestown be x\u00b0<br \/>\nLet the interior angles at Yorktown be 2x\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54545\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-math-Answers-Grade-8-ch3-angles-and-triangle-img_9-300x221.png\" alt=\"Big Ideas math Answers Grade 8 ch3 angles and triangle img_9\" width=\"300\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-math-Answers-Grade-8-ch3-angles-and-triangle-img_9-300x221.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-math-Answers-Grade-8-ch3-angles-and-triangle-img_9.png 502w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + 2x\u00b0 + 120\u00b0 = 180\u00b0<br \/>\n3x\u00b0 + 120\u00b0 = 180\u00b0<br \/>\n3x\u00b0 = 180\u00b0 &#8211; 120\u00b0<br \/>\n3x\u00b0 = 60\u00b0<br \/>\nx\u00b0 = 60\/3<br \/>\nx\u00b0 = 20\u00b0<br \/>\nThe interior angles at Jamestown be x\u00b0 = 20\u00b0<br \/>\nThe interior angles at Yorktown be 2x\u00b0 = 2(20)\u00b0 = 40\u00b0<\/p>\n<p>Question 8.<br \/>\nA helicopter travels from point C to point A to perform a medical supply drop. The helicopter then needs to land at point B. How many degrees should the helicopter turn at point A to travel towards point B? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-44.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 44\" width=\"211\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA helicopter travels from point C to point A to perform a medical supply drop.<br \/>\nThe helicopter then needs to land at point B.<br \/>\nA = 90\u00b0 + 32\u00b0<br \/>\nA = 122\u00b0<br \/>\nThus the helicopter should turn 122\u00b0 at point A to travel towards point B.<\/p>\n<h3><a id=\"Angles_of_Triangles_Homework_&amp;_Practice_3.2\"><\/a>Angles of Triangles Homework &amp; Practice 3.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Use the \ufb01gure to \ufb01nd the measure of the angle. Explain your reasoning.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-45.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 45\" width=\"252\" height=\"118\" \/><\/p>\n<p>Question 1.<br \/>\n\u22202<\/p>\n<p>Answer: 82\u00b0<\/p>\n<p>\u22202 and 82\u00b0 are alternate exterior angles formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nThus the measure of \u22202 is 82\u00b0<\/p>\n<p>Question 2.<br \/>\n\u22206<\/p>\n<p>Answer: 82\u00b0<\/p>\n<p>\u22206 and 82\u00b0 are vertical angles formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nThus the measure of \u22206 is 82\u00b0<\/p>\n<p>Question 3.<br \/>\n\u22204<\/p>\n<p>Answer: 82\u00b0<\/p>\n<p>\u22204 and 82\u00b0 are corresponding angles formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nThus the measure of \u22204 is 82\u00b0<\/p>\n<p>Question 4.<br \/>\n\u22201<\/p>\n<p>Answer: 98\u00b0<\/p>\n<p>\u22204 and 82\u00b0 are corresponding angles formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nThus the measure of \u22204 is 82\u00b0<br \/>\n\u22204 and \u22201 are supplementary angles<br \/>\n\u22204 + \u22201 = 180\u00b0<br \/>\n82\u00b0 + \u22201 = 180\u00b0<br \/>\n\u22201 = 180\u00b0 &#8211; 82\u00b0<br \/>\n\u22201 = 98\u00b0<\/p>\n<p><strong>You spin the spinner shown.<\/strong><\/p>\n<p>Question 5.<br \/>\nWhat are the favorable outcomes of spinning a number less than 4?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-46.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 46\" width=\"158\" height=\"155\" \/><\/p>\n<p>Answer: 1, 2, 3<\/p>\n<p>Explanation:<br \/>\nThe favorable outcome of spinning a number less than 4 is 1, 2, and 3.<\/p>\n<p>Question 6.<br \/>\nIn how many ways can spinning an odd number occur?<\/p>\n<p>Answer: two ways<br \/>\nOdd numbers = 1 and 3<br \/>\nSo, in two ways spinning an odd number can occur.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING PARALLEL LINES AND TRANSVERSALS<\/strong><br \/>\n<strong>Consider the \ufb01gure below.<\/strong> (See Exploration 2, p. 111.)<\/p>\n<p>Question 7.<br \/>\nUse a protractor to \ufb01nd the measures of the labeled angles.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-47.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 47\" width=\"361\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-47.png 361w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-47-300x171.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><\/p>\n<p>Answer:<br \/>\nUse a protractor to determine the measures of the angles A, B, C.<br \/>\nm\u2220A = 30\u00b0<br \/>\nm\u2220B = 105\u00b0<br \/>\nm\u2220C = 45\u00b0<br \/>\nm\u2220D = 150\u00b0<br \/>\nm\u2220E = 75\u00b0<br \/>\nm\u2220F = 105\u00b0<br \/>\nm\u2220G = 30\u00b0<\/p>\n<p>Question 8.<br \/>\nIs \u2220F an exterior angle of Triangle ABC ? Justify your answer.<\/p>\n<p>Answer:<br \/>\nAn exterior angle is the angle between one side of a triangle and the extension of an adjacent side. \u2220F is not an exterior angle of triangle ABC because it has a side of triangle ABC, but not the extension of the adjacent side DF.<\/p>\n<p><strong>USING INTERIOR ANGLE MEASURES<\/strong><br \/>\n<strong>Find the measures of the interior angles of the triangle.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-48.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 48\" width=\"167\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + 90\u00b0 + 30\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 120\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 120\u00b0<br \/>\nx\u00b0 = 60\u00b0<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-49.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 49\" width=\"165\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + 65\u00b0 + 40\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 105\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 105\u00b0<br \/>\nx\u00b0 = 75\u00b0<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-50.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 50\" width=\"147\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + 35\u00b0 + 45\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 80\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 80\u00b0<br \/>\nx\u00b0 = 100\u00b0<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-51.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 51\" width=\"177\" height=\"122\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + (x + 65)\u00b0 + 25\u00b0 = 180\u00b0<br \/>\nx\u00b0 + x\u00b0 + 65\u00b0 + 25\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + 90\u00b0 = 180\u00b0<br \/>\n2x\u00b0 = 180\u00b0 &#8211; 90\u00b0<br \/>\n2x\u00b0 = 90\u00b0<br \/>\nx\u00b0 = 90\u00b0\/2<br \/>\nx\u00b0 = 45\u00b0<br \/>\n(x + 65)\u00b0 = 45 + 65 = 110<br \/>\nx\u00b0 = 25\u00b0<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-52.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 52\" width=\"172\" height=\"101\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + (x &#8211; 44)\u00b0 + 48\u00b0 = 180\u00b0<br \/>\nx\u00b0 + x\u00b0 &#8211; 44\u00b0 + 48\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + 4\u00b0 = 180\u00b0<br \/>\n2x\u00b0 = 180\u00b0 &#8211; 4\u00b0<br \/>\n2x\u00b0 = 176\u00b0<br \/>\nx\u00b0 = 176\u00b0\/2<br \/>\nx\u00b0 = 88\u00b0<br \/>\n(x &#8211; 44)\u00b0 = 88 &#8211; 44 = 44<br \/>\nx\u00b0 = 44\u00b0<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-53.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 53\" width=\"138\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + (x &#8211; 11)\u00b0 + 73\u00b0 = 180\u00b0<br \/>\nx\u00b0 + x\u00b0 &#8211; 11\u00b0 + 73\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + 62\u00b0 = 180\u00b0<br \/>\n2x\u00b0 = 180\u00b0 &#8211; 62\u00b0<br \/>\n2x\u00b0 = 118\u00b0<br \/>\nx\u00b0 = 118\u00b0\/2<br \/>\nx\u00b0 = 59\u00b0<br \/>\n(x &#8211; 11)\u00b0 = 59 &#8211; 11 = 48<br \/>\nx\u00b0 = 48\u00b0<\/p>\n<p><strong>FINDING EXTERIOR ANGLE MEASURES<\/strong><br \/>\n<strong>Find the measure of the exterior angle.<\/strong><\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-54.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 54\" width=\"168\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nx\u00b0 = 38\u00b0 + 90\u00b0<br \/>\nx\u00b0 = 128\u00b0<br \/>\nThe measure of exterior angle is 128\u00b0<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-55.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 55\" width=\"126\" height=\"135\" \/><\/p>\n<p>Answer:<br \/>\nk\u00b0 = 64\u00b0 + 76\u00b0<br \/>\nk\u00b0 = 140\u00b0<br \/>\nThe measure of an exterior angle is 140\u00b0<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-56.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 56\" width=\"175\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\n2a\u00b0 = (a + 10\u00b0) + 44\u00b0<br \/>\n2a\u00b0 = a + 54\u00b0<br \/>\n2a\u00b0 &#8211; a\u00b0 = 54<br \/>\na\u00b0 = 54<br \/>\nThe measure of the exterior angle = 2a = 2(54\u00b0) = 108\u00b0<\/p>\n<p>Question 18.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA tornado is located between city hall and a cell phone tower and is heading towards the cell phone tower. By what angle does the tornado\u2019s direction need to change so that it passes over the radar station instead? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-57.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 57\" width=\"338\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-57.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-57-300x118.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + 75\u00b0 + 75\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 150\u00b0 &#8211; 150\u00b0 = 180\u00b0 &#8211; 150\u00b0<br \/>\nx\u00b0 = 30\u00b0<br \/>\nThus the angle that tornado direction needs to change is 30\u00b0.<\/p>\n<p>Question 19.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the measure of the exterior angle shown. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-58.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 58\" width=\"446\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-58.png 446w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-58-300x110.png 300w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><\/p>\n<p>Answer:<br \/>\nYour friend is not correct because the measure of the exterior angle is equal to the sum of two non-adjacent interior angles.<\/p>\n<p>Question 20.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe ratio of the interior angle measures of a triangle is 2 : 3 : 5. What are the angle measures?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-59.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 59\" width=\"209\" height=\"192\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\n2x\u00b0 + 3x\u00b0 + 5x\u00b0 = 180\u00b0<br \/>\n10x\u00b0 = 180\u00b0<br \/>\nx = 180\/10<br \/>\nx = 18\u00b0<br \/>\n2x\u00b0 = 2(18\u00b0) = 36\u00b0<br \/>\n3x\u00b0 = 3(18) = 54\u00b0<br \/>\n5x\u00b0 = 5(18) = 90\u00b0<\/p>\n<p>Question 21.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe support for a window air-conditioning unit forms a triangle and an exterior angle. What is the measure of the exterior angle?<\/p>\n<p>Answer:<br \/>\nThe measure of the exterior angle DBC is<br \/>\nm\u2220DBC = m\u2220ABC + m\u2220ACB<br \/>\nm\u2220ABC + m\u2220ACB = 90\u00b0<br \/>\n5x &#8211; 6 + 3x = 90<br \/>\n8x &#8211; 6 = 90<br \/>\n8x = 90 + 6<br \/>\n8x = 96<br \/>\nx = 96\/8<br \/>\nx = 12<br \/>\nm\u2220DBC = m\u2220BAC+ m\u2220ACB<br \/>\n= 90\u00b0 + 3(12)\u00b0<br \/>\n= 126\u00b0<\/p>\n<p>Question 22.<br \/>\n<strong>REASONING<\/strong><br \/>\nA triangle has an exterior angle with a measure of 120\u00b0. Can you determine the measures of the interior angles? Explain.<\/p>\n<p>Answer:<br \/>\nA triangle has an exterior angle with a measure of 120\u00b0<br \/>\nm\u2220ACB = m\u2220A + m\u2220B<br \/>\nm\u2220A + m\u2220B = 120\u00b0<br \/>\nAccording to the exterior angles<br \/>\nWe have<br \/>\nm\u2220C + m\u2220ACD = 180\u00b0<br \/>\nm\u2220C + 120\u00b0 = 180\u00b0<br \/>\nm\u2220C = 180\u00b0 &#8211; 120\u00b0<br \/>\nm\u2220C = 60\u00b0<\/p>\n<p><strong>ANGLES OF TRIANGLES<\/strong><\/p>\n<p><strong>Determine whether the statement is always, sometimes, or never true. Explain your reasoning.<\/strong><\/p>\n<p>Question 23.<br \/>\nGiven three angle measures, you can construct a triangle.<\/p>\n<p>Answer:<br \/>\nWe can construct a triangle if the sum of the measure of the 3 angles is 180\u00b0.<br \/>\nAs a matter of fact, if the sum of the measures of the 3 angles is 180\u00b0<br \/>\nWe can build an infinity of triangles that are similar.<\/p>\n<p>Question 24.<br \/>\nThe acute interior angles of a right triangle are complementary.<\/p>\n<p>Answer:<br \/>\nLet A, B, C be the angles of a right triangle with m\u2220A = 90\u00b0<br \/>\nm\u2220A + m\u2220B + m\u2220C = 180\u00b0<br \/>\n90\u00b0 + m\u2220B + m\u2220C = 180\u00b0<br \/>\nm\u2220B + m\u2220C = 180\u00b0 &#8211; 90\u00b0<br \/>\nm\u2220B + m\u2220C = 90\u00b0<br \/>\nThis means \u2220B and \u2220C are complementary.<\/p>\n<p>Question 25.<br \/>\nA triangle has more than one vertex with an acute exterior angle.<\/p>\n<p>Answer:<br \/>\nAn exterior angle of a triangle and the adjacent triangle&#8217;s angle are complementary. If an exterior angle is acute, it means the adjacent triangle&#8217;s angle is obtuse.<br \/>\nSince we are given that more than one exterior angle is acute, it means the triangle would have more than one obtuse angle, which is impossible.<br \/>\nThe statement is never true.<\/p>\n<p>Question 26.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nUsing the \ufb01gure at the right, show that z = x + y. (Hint: Find two equations involving w.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-60.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 60\" width=\"192\" height=\"93\" \/><\/p>\n<p>Answer:<br \/>\nThe angles z and w are supplementary<br \/>\nz + w = 180\u00b0<br \/>\nThe sum of a triangle is 180\u00b0<br \/>\nx + y + w = 180\u00b0<br \/>\nz = 180\u00b0 &#8211; w<br \/>\nx + y = 180\u00b0 &#8211; w<br \/>\nz = x + y<\/p>\n<h3><a id=\"Lesson_3.3_Angles_of_Polygons\"><\/a>Lesson 3.3 Angles of Polygons<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Work with a partner. In parts (a)-(f), use what you know about the interior angle measures of triangles to \ufb01nd the sum of the interior angle measures of each \ufb01gure.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-61.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 3 Angles and Triangles 61\" width=\"681\" height=\"457\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-61.png 681w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-3-Angles-and-Triangles-61-300x201.png 300w\" sizes=\"(max-width: 681px) 100vw, 681px\" \/><br \/>\n<strong>g. REPEATED REASONING<\/strong><br \/>\nUse your results in parts (a)\u2013(f) to complete the table. Then write an equation that represents the sum of the interior angle measures of a polygon with n sides.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-62.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 62\" width=\"521\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-62.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-62-300x63.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p>Answer:<\/p>\n<p><strong>3.3 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the sum of the interior angle measures of the green polygon.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-63.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 63\" width=\"184\" height=\"178\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (7 &#8211; 2) . 180\u00b0<br \/>\nS = 5 . 180\u00b0<br \/>\nS = 900\u00b0<br \/>\nThus the sum of the interior angle measure is 900\u00b0<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-64.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 64\" width=\"242\" height=\"166\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (6 &#8211; 2) . 180\u00b0<br \/>\nS = 4 . 180\u00b0<br \/>\nS = 720\u00b0<br \/>\nThus the sum of the interior angle measure is 720\u00b0<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to \ufb01nd the sum of the interior measures of a polygon.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-65.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 65\" width=\"179\" height=\"185\" \/><\/p>\n<p>Answer:<br \/>\nSteps to find the sum of the interior measurements of the polygon:<br \/>\n1. Count the number of sides of the polygon.<br \/>\n2. Subtract the number of sides by 2.<br \/>\n3. Multiply the result of the subtraction by 180\u00b0<\/p>\n<p>Question 6.<br \/>\n<strong>FINDING THE SUM OF INTERIOR ANGLE MEASURES<\/strong><br \/>\nFind the sum of the interior angle measures of the green polygon.<\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (4 &#8211; 2) . 180\u00b0<br \/>\nS = 2 . 180\u00b0<br \/>\nS = 360\u00b0<br \/>\nThus the sum of the interior angle measure is 360\u00b0<\/p>\n<p><strong>FINDING AN INTERIOR ANGLE MEASURE<\/strong><\/p>\n<p><strong>Find the value of x.<\/strong><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-66.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 66\" width=\"182\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (5 &#8211; 2) . 180\u00b0<br \/>\nS = 3 . 180\u00b0<br \/>\nS = 540\u00b0<br \/>\nThus the sum of the interior angle measure is 540\u00b0<br \/>\nx\u00b0 + 160\u00b0 + 110\u00b0 + 105\u00b0 + 95\u00b0 = 540\u00b0<br \/>\nx\u00b0 + 470\u00b0 = 540\u00b0<br \/>\nx\u00b0 = 540\u00b0 &#8211; 470\u00b0<br \/>\nx\u00b0 = 70\u00b0<br \/>\nThus the value of x is 70\u00b0.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-67.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 67\" width=\"187\" height=\"143\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (9 &#8211; 2) . 180\u00b0<br \/>\nS = 7 . 180\u00b0<br \/>\nS = 1260\u00b0<br \/>\nThus the sum of the interior angle measure is 1260\u00b0<br \/>\nx\u00b0 + 165\u00b0 + 155\u00b0 + 150\u00b0 + 140\u00b0 + 135\u00b0 + 130\u00b0 + 125\u00b0 + 110\u00b0 = 1260\u00b0<br \/>\nx\u00b0 + 1105\u00b0 = 1260\u00b0<br \/>\nx\u00b0 = 1260\u00b0 &#8211; 1105\u00b0<br \/>\nx\u00b0 = 155\u00b0<br \/>\nThus the value of x is 155\u00b0<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\nA company installs an octagonal swimming pool.<br \/>\na. Find the value of a for the pool shown at the left.<\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (8 &#8211; 2) . 180\u00b0<br \/>\nS = 6 . 180\u00b0<br \/>\nS = 1080\u00b0<br \/>\nThus the sum of the interior angle measure is 1080\u00b0<br \/>\na\u00b0 + 120\u00b0 + a\u00b0 + 120\u00b0 + a\u00b0 + 120\u00b0 + a\u00b0 + 120\u00b0 = 1080\u00b0<br \/>\n4a\u00b0 + 480\u00b0 = 1080\u00b0<br \/>\n4a\u00b0 = 1080\u00b0 &#8211; 480\u00b0<br \/>\n4a\u00b0 = 600\u00b0<br \/>\na\u00b0 = 600\/4<br \/>\na\u00b0 = 150\u00b0<br \/>\nThus the value of x is 150\u00b0.<\/p>\n<p>b. The company installs a different pool that is also in the shape of an octagon. The second pool has twice the length and one-third the width of the \ufb01rst pool. Are the sums of the interior angles of the pools different? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-67.1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 67.1\" width=\"220\" height=\"147\" \/><\/p>\n<p>Answer:<br \/>\nNo for any octagon the sum of the interior angles is 1080 degrees.<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA Bronze Star Medal A is shown.<br \/>\na. How many interior angles are there?<\/p>\n<p>Answer: 10 interior angles are there<\/p>\n<p>b. What is the sum of the interior angle measures?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-68.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 68\" width=\"188\" height=\"247\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (10 &#8211; 2) . 180\u00b0<br \/>\nS = 8 . 180\u00b0<br \/>\nS = 1440\u00b0<br \/>\nThus the sum of the interior angle measure is 1440\u00b0<\/p>\n<h3><a id=\"Angles_of_Polygons_Homework_&amp;_Practice_3.3\"><\/a>Angles of Polygons Homework &amp; Practice 3.3<\/h3>\n<p><strong>Find the value of x.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-69.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 69\" width=\"107\" height=\"97\" \/><\/p>\n<p>Answer: 60\u00b0<\/p>\n<p>Explanation:<br \/>\nSum of all the angles = 180\u00b0<br \/>\nx\u00b0 + 60\u00b0 + 60\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 120\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 120\u00b0<br \/>\nx\u00b0 = 60\u00b0<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-70.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 70\" width=\"134\" height=\"101\" \/><\/p>\n<p>Answer: 45\u00b0<\/p>\n<p>Explanation:<br \/>\nSum of all the angles = 180\u00b0<br \/>\nx\u00b0 + x\u00b0 + 90\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + 90\u00b0 = 180\u00b0<br \/>\n2x\u00b0 = 180\u00b0 &#8211; 90\u00b0<br \/>\n2x\u00b0 = 90\u00b0<br \/>\nx\u00b0 = 45\u00b0<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-71.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 71\" width=\"176\" height=\"102\" \/><\/p>\n<p>Answer: 113\u00b0<\/p>\n<p>Explanation:<br \/>\nx\u00b0 = 65\u00b0 + 48\u00b0<br \/>\nx\u00b0 = 113\u00b0<br \/>\nThus the measure of an exterior angle is 113\u00b0<\/p>\n<p><strong>Solve the proportion.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-72.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 72\" width=\"70\" height=\"51\" \/><\/p>\n<p>Answer: 9<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{x}{12}\\) = \\(\\frac{3}{4}\\)<br \/>\n12 . \\(\\frac{x}{12}\\) = \\(\\frac{3}{4}\\) . 12<br \/>\nx = 3 . 3<br \/>\nx = 9<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-73.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 73\" width=\"62\" height=\"46\" \/><\/p>\n<p>Answer: 2<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{14}{21}\\) = \\(\\frac{x}{3}\\)<br \/>\n3 . \\(\\frac{14}{21}\\) = \\(\\frac{x}{3}\\) . 3<br \/>\nx = 2<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-74.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 74\" width=\"63\" height=\"55\" \/><\/p>\n<p>Answer: 3<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{9}{x}\\) = \\(\\frac{6}{2}\\)<br \/>\n2. \\(\\frac{9}{x}\\) = 6<br \/>\n18 = 6x<br \/>\nx = 3<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>EXPLORING INTERIOR ANGLES OF POLYGONS<\/strong><br \/>\n<strong>Use triangles to \ufb01nd the sum of the interior angle measures of the polygon.<\/strong> (See Exploration 1, p. 117.)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-75.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 75\" width=\"108\" height=\"111\" \/><\/p>\n<p>Answer: 360\u00b0<\/p>\n<p>Explanation:<br \/>\nNumber of sides = 4<br \/>\nNumber of interior triangles in the given figure = 2<br \/>\nThe Sum of the measures of the interior angles using triangle = 2 . 180\u00b0 = 360\u00b0<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-76.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 76\" width=\"122\" height=\"120\" \/><\/p>\n<p>Answer: 1260\u00b0<\/p>\n<p>Explanation:<br \/>\nNumber of sides = 9<br \/>\nNumber of interior triangles in the given figure = 7<br \/>\nThe Sum of the measures of the interior angles using triangle = 7 . 180\u00b0 = 1260\u00b0<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-77.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 77\" width=\"80\" height=\"113\" \/><\/p>\n<p>Answer: 540\u00b0<\/p>\n<p>Explanation:<br \/>\nNumber of sides = 5<br \/>\nNumber of interior triangles in the given figure = 3<br \/>\nThe Sum of the measures of the interior angles using triangle = 3 . 180\u00b0 = 540\u00b0<\/p>\n<p><strong>FINDING THE SUM OF INTERIOR ANGLE MEASURES<\/strong><br \/>\n<strong>Find the sum of the interior angle measures of the polygon.<\/strong><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-78.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 78\" width=\"161\" height=\"95\" \/><\/p>\n<p>Answer: 360\u00b0<\/p>\n<p>Explanation:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (4- 2) . 180\u00b0<br \/>\nS = 2 . 180\u00b0<br \/>\nS = 360\u00b0<br \/>\nThus the sum of the interior angle measure is 360\u00b0<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-79.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 79\" width=\"129\" height=\"126\" \/><\/p>\n<p>Answer: 1080\u00b0<\/p>\n<p>Explanation:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (8- 2) . 180\u00b0<br \/>\nS = 6 . 180\u00b0<br \/>\nS = 1080\u00b0<br \/>\nThus the sum of the interior angle measure is 1080\u00b0<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-80.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 80\" width=\"130\" height=\"119\" \/><\/p>\n<p>Answer: 1260\u00b0<\/p>\n<p>Explanation:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (9- 2) . 180\u00b0<br \/>\nS = 7 . 180\u00b0<br \/>\nS = 1260\u00b0<br \/>\nThus the sum of the interior angle measure is 1260\u00b0<\/p>\n<p>Question 13.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the sum of the interior angle measures of a 13-gon. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-81.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 81\" width=\"164\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nTo find the sum of the interior angle measures he should subtract 2 from the number of sides of the polygon and then multiply by 180\u00b0<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nBy this, we can say that your friend is not correct.<\/p>\n<p><strong>FINDING AN INTERIOR ANGLE MEASURE<\/strong><br \/>\n<strong>Find the value of x.<\/strong><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-82.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 82\" width=\"198\" height=\"77\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (4- 2) . 180\u00b0<br \/>\nS = 2 . 180\u00b0<br \/>\nS = 360\u00b0<br \/>\nThus the sum of the interior angle measure is 360\u00b0<br \/>\nx\u00b0 + 155\u00b0 + 25\u00b0 + 137\u00b0 = 360\u00b0<br \/>\nx\u00b0 + 317\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\u00b0 &#8211; 317\u00b0<br \/>\nx\u00b0 = 43\u00b0<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-83.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 83\" width=\"148\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (6- 2) . 180\u00b0<br \/>\nS = 4 . 180\u00b0<br \/>\nS = 720\u00b0<br \/>\nThus the sum of the interior angle measure is 720\u00b0<br \/>\nx\u00b0 + x\u00b0 + x\u00b0 + x\u00b0 + 90\u00b0 + 90\u00b0 = 720\u00b0<br \/>\n4x\u00b0 + 180\u00b0 = 720\u00b0<br \/>\n4x\u00b0 = 720\u00b0 &#8211; 180\u00b0<br \/>\n4x\u00b0 = 540\u00b0<br \/>\nx\u00b0 = 540\/4<br \/>\nx\u00b0 = 135\u00b0<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-84.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 84\" width=\"170\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (6- 2) . 180\u00b0<br \/>\nS = 4 . 180\u00b0<br \/>\nS = 720\u00b0<br \/>\nThus the sum of the interior angle measure is 720\u00b0<br \/>\n3x\u00b0 + 45\u00b0 + 135\u00b0 + x\u00b0 + 135\u00b0 + 45\u00b0 = 720\u00b0<br \/>\n4x\u00b0 + 360\u00b0 = 720\u00b0<br \/>\n4x\u00b0 = 720\u00b0 &#8211; 360\u00b0<br \/>\n4x\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\/4<br \/>\nx\u00b0 = 90\u00b0<\/p>\n<p><strong>FINDING A MEASURE<\/strong><br \/>\n<strong>Find the measure of each interior angle of the regular polygon.<\/strong><\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-85.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 85\" width=\"167\" height=\"177\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (3- 2) . 180\u00b0<br \/>\nS = 1 . 180\u00b0<br \/>\nS = 180\u00b0<br \/>\nThus the sum of the interior angle measure is 180\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 3.<br \/>\n180 \u00f7 3 = 60\u00b0<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-86.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 86\" width=\"199\" height=\"188\" \/><\/p>\n<p>Answer:<\/p>\n<p>S = (n &#8211; 2) . 180\u00b0<br \/>\nS = (9 &#8211; 2) . 180\u00b0<br \/>\nS = 7 . 180\u00b0<br \/>\nS = 1260\u00b0<br \/>\nThus the sum of the interior angle measure is 1260\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 9.<br \/>\n1260 \u00f7 9 = 140\u00b0<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-87.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 87\" width=\"164\" height=\"198\" \/><\/p>\n<p>Answer:<\/p>\n<p>S = (n &#8211; 2) . 180\u00b0<br \/>\nS = (12 &#8211; 2) . 180\u00b0<br \/>\nS = 10 . 180\u00b0<br \/>\nS = 1800\u00b0<br \/>\nThus the sum of the interior angle measure is 1800\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 12.<br \/>\n1800 \u00f7 12 = 150\u00b0<\/p>\n<p>Question 20.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the measure of each interior angle of a regular 20-gon. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-88.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 88\" width=\"194\" height=\"217\" \/><\/p>\n<p>Answer:<br \/>\nNo, my friend is not correct because to find the measure of each interior angle of a regular 20-gon, he should divide the sum of the measured interior angles by the number of interior angles, in this case, 20 but your friend divide it by 18 so he is not correct.<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA \ufb01rehydrant bolt is in the shape of a regular pentagon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-89.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 89\" width=\"132\" height=\"193\" \/><br \/>\na. What is the measure of each interior angle?<\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (5- 2) . 180\u00b0<br \/>\nS = 3 . 180\u00b0<br \/>\nS = 540\u00b0<br \/>\nThus the sum of the interior angle measure is 540\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 5.<br \/>\n540\u00f7 5 = 108\u00b0<\/p>\n<p><strong>b. RESEARCH<\/strong><br \/>\nWhy are \ufb01rehydrants made this way?<\/p>\n<p>Question 22.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe interior angles of a regular polygon each measure 165\u00b0. How many sides does the polygon have?<\/p>\n<p>Answer:<br \/>\n(n &#8211; 2) . 180 = 165 . n<br \/>\n180n &#8211; 360 = 165n<br \/>\n180n &#8211; 360 + 360 &#8211; 165n = 165n + 360 &#8211; 165n<br \/>\n15n = 360<br \/>\nn = 360\/15<br \/>\nn = 24<br \/>\nTherefore the polygon has 24 sides<\/p>\n<p>Question 23.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nA molecule can be represented by a polygon with interior angles that each measure 120\u00b0. What polygon represents the molecule? Does the polygon have to be regular? Justify your answers.<\/p>\n<p>Answer:<br \/>\n(n &#8211; 2) . 180 = 120 . n<br \/>\n180n &#8211; 360 = 120n<br \/>\n180n &#8211; 120n = 360<br \/>\n60n = 360<br \/>\nn = 6<\/p>\n<p>Question 24.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe border of a Susan B. Anthony dollar is in the shape of a regular polygon.<br \/>\na. How many sides does the polygon have?<\/p>\n<p>Answer: The polygon has 11 sides.<\/p>\n<p>b. What is the measure of each interior angle of the border? Round your answer to the nearest degree.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-91.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 91\" width=\"140\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (11 &#8211; 2) . 180\u00b0<br \/>\nS = 9 . 180\u00b0<br \/>\nS = 1620\u00b0<br \/>\nThus the sum of the interior angle measure is 1620\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 11.<br \/>\n1620 \u00f7 11 = 147\u00b0<\/p>\n<p>Question 25.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe center of the stained glass window is in the shape of a regular polygon. What are the measures of the interior angles of the green triangle?<\/p>\n<p>Answer:<br \/>\n(n-2)180\u00b0\/n = (8-2)180\u00b0\/8 = 135\u00b0<br \/>\nm\u2220OAB = m\u2220OBA = 135\/2 = 67.5\u00b0<br \/>\nm\u2220AOB + m\u2220OAB + m\u2220OBA = 180\u00b0<br \/>\nm\u2220AOB + 67.5\u00b0 + 67.5\u00b0 = 180\u00b0<br \/>\nm\u2220AOB + 135\u00b0 = 180\u00b0<br \/>\nm\u2220AOB = 180\u00b0 &#8211; 135\u00b0<br \/>\nm\u2220AOB = 45\u00b0<\/p>\n<p>Question 26.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nDraw a pentagon that has two right interior angles, two 45\u00b0 interior angles, and one 270\u00b0 interior angle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-92.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 92\" width=\"207\" height=\"203\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-8th-Grade-Solution-Key-Ch-3-Angles-and-Triangles-img_9-300x254.png\" alt=\"Big Ideas Math 8th Grade Solution Key Ch 3 Angles and Triangles img_9\" width=\"300\" height=\"254\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-8th-Grade-Solution-Key-Ch-3-Angles-and-Triangles-img_9-300x254.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-8th-Grade-Solution-Key-Ch-3-Angles-and-Triangles-img_9.png 444w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-8th-Grade-Solution-Key-Ch-3-Angles-and-Triangles-img_10-300x254.png\" alt=\"Big Ideas Math 8th Grade Solution Key Ch 3 Angles and Triangles img_10\" width=\"300\" height=\"254\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-8th-Grade-Solution-Key-Ch-3-Angles-and-Triangles-img_10-300x254.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-8th-Grade-Solution-Key-Ch-3-Angles-and-Triangles-img_10.png 444w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 27.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe \ufb02oor of a gazebo is in the shape of a heptagon, a seven-sided polygon. Four of the interior angles measure 135\u00b0. The other interior angles have equal measures. Find their measures.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-93.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 93\" width=\"186\" height=\"162\" \/><\/p>\n<p>Answer:<br \/>\nThe given polygon has 7 sides.<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (7 &#8211; 2) . 180\u00b0<br \/>\nS = 5 . 180\u00b0<br \/>\nS = 900\u00b0<br \/>\nThus the sum of the interior angle measure is 900\u00b0<br \/>\n4 . 135\u00b0 + 3 . x\u00b0 = 900\u00b0<br \/>\n540\u00b0 + 3x\u00b0 = 900\u00b0<br \/>\n3x\u00b0 = 900\u00b0 &#8211; 540\u00b0<br \/>\n3x\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\/3<br \/>\nx\u00b0 = 120\u00b0<\/p>\n<h3><a id=\"Lesson_3.4_Using_Similar_Triangles\"><\/a>Lesson 3.4 Using Similar Triangles<\/h3>\n<p><strong>Using Similar Triangles<\/strong><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Work with a partner. Use geometry software.<\/strong><br \/>\na. Draw a triangle that has a 50\u00b0 angle and a 30\u00b0 angle. Then draw a triangle that is either larger or smaller that has the same two angle measures. Are the triangles congruent? similar? Explain your reasoning.<br \/>\na. Choose any two angle measures whose sum is less than 180\u00b0. Repeat part(a) using the angle measures you chose.<br \/>\nc. Compare your results in parts (a) and (b) with other pairs of students. Make a conjecture about two triangles that have two pairs of congruent angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-93.1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 93.1\" width=\"257\" height=\"238\" \/><\/p>\n<p>Answer:<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Using Indirect Measurement<\/strong><br \/>\n<strong>Work with a partner. Use the fact that two rays from the Sun are parallel to make a plan for how to \ufb01nd the height of the \ufb02agpole. Explain your reasoning.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-94.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 94\" width=\"724\" height=\"399\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-94.png 724w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-94-300x165.png 300w\" sizes=\"(max-width: 724px) 100vw, 724px\" \/><\/p>\n<p>Answer:<\/p>\n<p><strong>3.4 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Tell whether the triangles are similar. Explain.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-95.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 95\" width=\"210\" height=\"137\" \/><\/p>\n<p>Answer: No<\/p>\n<p>Explanation:<br \/>\nx\u00b0 + 28\u00b0 + 80\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 108\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 108\u00b0<br \/>\nx\u00b0 = 72\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/BIM-Grade-8-Answer-Key-Chapter-3-Angles-and-triangles-img_11-300x182.png\" alt=\"BIM Grade 8 Answer Key Chapter 3 Angles and triangles img_11\" width=\"300\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/BIM-Grade-8-Answer-Key-Chapter-3-Angles-and-triangles-img_11-300x182.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/BIM-Grade-8-Answer-Key-Chapter-3-Angles-and-triangles-img_11.png 564w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\ny\u00b0 + 28\u00b0 + 71\u00b0 = 180\u00b0<br \/>\ny\u00b0 + 99\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 99\u00b0<br \/>\ny\u00b0 = 81\u00b0<br \/>\nThe triangles do not have two pairs of congruent angles.<br \/>\nSo, the triangles are not similar.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-96.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 96\" width=\"233\" height=\"131\" \/><\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\nx\u00b0 + 66\u00b0 + 90\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 156\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 156\u00b0<br \/>\nx\u00b0 = 24\u00b0<br \/>\ny\u00b0 + 24\u00b0 + 90\u00b0 = 180\u00b0<br \/>\ny\u00b0 + 114\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 114\u00b0<br \/>\ny\u00b0 = 66\u00b0<br \/>\nThe triangles have two pairs of congruent angles.<br \/>\nThus the triangles are similar.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 3.<br \/>\nCan you determine whether \u25b3PQR and \u25b3TSRand are similar? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-97.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 97\" width=\"190\" height=\"144\" \/><\/p>\n<p>Answer: No<\/p>\n<p>Explanation:<br \/>\nWe are not given any information about the lengths of the sides either, therefore with only a pair of congruent angles, we cannot tell whether the triangles are similar.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 4.<br \/>\n<strong>IDENTIFYING SIMILAR TRIANGLES<\/strong><br \/>\nTell whether the triangles are similar. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-98.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 98\" width=\"243\" height=\"148\" \/><\/p>\n<p>Answer: Yes<\/p>\n<p>Explanation:<br \/>\nx\u00b0 + 54\u00b0 + 63\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 107\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 107\u00b0<br \/>\nx\u00b0 = 63\u00b0<\/p>\n<p>Question 5.<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-32079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-98.1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 98.1\" width=\"498\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-98.1.png 498w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-98.1-300x66.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-99.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 99\" width=\"132\" height=\"177\" \/><\/p>\n<p>Answer: Option B<\/p>\n<p>Explanation:<br \/>\n\u0394PQR and \u0394TSR are congruent as TS || PQ leads to two pairs of correspondent congruent angles.<br \/>\n\u0394PQR is a dilation of \u0394TSR because their sides are proportional, the constant of proportionality being greater than 1.<br \/>\n\u0394PQR is a scale drawing of \u0394TSR because their sides are proportional.<br \/>\nThe question that does not fit is<br \/>\n&#8220;Are \u0394PQR and \u0394TSR the same size and shape?&#8221;<br \/>\nbecause the triangles do not have the same size, but they have the same shape.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 6.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nEngineers plan to construct an aqueduct to transport water from the top of a ridge to farmland. A portion of the project is complete. Find the length of the entire aqueduct.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-100.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 100\" width=\"360\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-100.png 360w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-100-300x138.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-101.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 101\" width=\"212\" height=\"189\" \/><\/p>\n<p>Answer:<br \/>\nAqueduct\/2.6 = 5\/1<br \/>\nAqueduct = 5 \u00d7 2.6<br \/>\nAqueduct = 13<br \/>\nThus the length of the Aqueduct is 13 km.<\/p>\n<p>Question 7.<br \/>\nYou want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point Y? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-102.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 102\" width=\"231\" height=\"163\" \/><\/p>\n<p>Answer:<br \/>\na\/10 = 3\/6<br \/>\n6 \u00d7 a = 3 \u00d7 10<br \/>\n6a = 30<br \/>\na = 30\/6<br \/>\na = 5<br \/>\nThe length from point Z to point Y is 5 miles.<br \/>\nTime to travel from point Z to point Y = 5\/3.5 = 1.56 hour<\/p>\n<h3><a id=\"Using_Similar_Triangles_Homework_&amp;_Practice_3.4\"><\/a>Using Similar Triangles Homework &amp; Practice 3.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the measure of each interior angle of the regular polygon.<\/strong><\/p>\n<p>Question 1.<br \/>\noctagon<\/p>\n<p>Answer: The measure of each interior angle is 135\u00b0<\/p>\n<p>Explanation:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (8- 2) . 180\u00b0<br \/>\nS = 6 . 180\u00b0<br \/>\nS = 1080\u00b0<br \/>\nThus the sum of the interior angle measure is 1080\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 8.<br \/>\n1080\u00f7 8= 135\u00b0<\/p>\n<p>Question 2.<br \/>\ndecagon<\/p>\n<p>Answer: The measure of each exterior angle is 144\u00b0<\/p>\n<p>Explanation:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (10 &#8211; 2) . 180\u00b0<br \/>\nS = 8 . 180\u00b0<br \/>\nS = 1440\u00b0<br \/>\nThus the sum of the interior angle measure is 1440\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 10.<br \/>\n1440\u00f7 10= 144\u00b0<\/p>\n<p>Question 3.<br \/>\n18-gon<\/p>\n<p>Answer: The measure of each interior angle is 160\u00b0<\/p>\n<p>Explanation:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (18- 2) . 180\u00b0<br \/>\nS = 16 . 180\u00b0<br \/>\nS = 2880\u00b0<br \/>\nThus the sum of the interior angle measure is 2880\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 18.<br \/>\n2880 \u00f7 18= 160\u00b0<\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><\/p>\n<p>Question 4.<br \/>\n3.5 + y = -1<\/p>\n<p>Answer:<br \/>\nGiven the equation<br \/>\n3.5 + y = -1<br \/>\ny = -1 &#8211; 3.5<br \/>\ny = -4.5<\/p>\n<p>Question 5.<br \/>\n9x = 54<\/p>\n<p>Answer:<br \/>\nGiven the equation<br \/>\n9x = 54<br \/>\nx = 54\/9<br \/>\nx = 6<\/p>\n<p>Question 6.<br \/>\n-4 = \\(\\frac{2}{7}\\)p<\/p>\n<p>Answer:<br \/>\nGiven the equation<br \/>\n-4 = \\(\\frac{2}{7}\\)p<br \/>\n-4 \u00d7 7 = 2p<br \/>\n2p = -28<br \/>\np = -28\/2<br \/>\np = -14<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>CREATING SIMILAR TRIANGLES<\/strong><br \/>\n<strong>Draw a triangle that is either larger or smaller than the one given and has two of the same angle measures. Explain why the new triangle is similar to the original triangle.<\/strong> (See Exploration 1, p. 123.)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-103.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 103\" width=\"236\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/BIM-Answers-for-Grade-8-chapter-3-img_12-196x300.png\" alt=\"BIM Answers for Grade 8 chapter 3 img_12\" width=\"196\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/BIM-Answers-for-Grade-8-chapter-3-img_12-196x300.png 196w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/BIM-Answers-for-Grade-8-chapter-3-img_12.png 222w\" sizes=\"(max-width: 196px) 100vw, 196px\" \/><br \/>\nThe above triangle and the given triangle are similar because the two angles in both the triangles are the same so the third angle is also the same.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-104.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 104\" width=\"149\" height=\"96\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-104.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 104\" width=\"149\" height=\"96\" \/><br \/>\nThe above triangle and the given triangle are similar because the two angles in both the triangles are the same so the third angle is also the same.<\/p>\n<p><strong>IDENTIFYING SIMILAR TRIANGLES<\/strong><br \/>\n<strong>Tell whether the triangles are similar. Explain.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-105.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 105\" width=\"268\" height=\"122\" \/><\/p>\n<p>Answer: The triangles have two pairs of congruent angles.<br \/>\nSo, the third angles are congruent, and the triangles are similar.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-106.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 106\" width=\"185\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nx\u00b0 + 36\u00b0 + 72\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 108\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 108\u00b0<br \/>\nx\u00b0 = 72\u00b0<br \/>\ny\u00b0 + 33\u00b0 + 72\u00b0 = 180\u00b0<br \/>\ny\u00b0 + 105\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 105\u00b0<br \/>\ny\u00b0 = 72\u00b0<br \/>\nThe triangles do not have two pairs of congruent angles.<br \/>\nTherefore the triangles are not similar.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-107.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 107\" width=\"257\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nx\u00b0 + 64\u00b0 + 85\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 149\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 149\u00b0<br \/>\nx\u00b0 = 31\u00b0<br \/>\ny\u00b0 + 26\u00b0 + 85\u00b0 = 180\u00b0<br \/>\ny\u00b0 + 111\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 111\u00b0<br \/>\ny\u00b0 = 69\u00b0<br \/>\nThe triangles do not have two pairs of congruent angles.<br \/>\nTherefore the triangles are not similar.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-108.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 108\" width=\"246\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nx\u00b0 + 48\u00b0 + 81\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 129\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 129\u00b0<br \/>\nx\u00b0 = 51\u00b0<br \/>\ny\u00b0 + 48\u00b0 + 51\u00b0 = 180\u00b0<br \/>\ny\u00b0 + 99\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 99\u00b0<br \/>\ny\u00b0 = 81\u00b0<br \/>\nThe triangles have two pairs of congruent angles.<br \/>\nTherefore the triangles are similar.<\/p>\n<p>Question 13.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nWhich of the rulers are similar in shape? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-109.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 109\" width=\"444\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-109.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-109-300x113.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Answer:<br \/>\n2x + 90 = 180\u00b0<br \/>\n2x = 180 &#8211; 90\u00b0<br \/>\n2x = 90\u00b0<br \/>\nx = 90\/2<br \/>\nx = 45\u00b0<br \/>\nThe ruler on the left and the ruler on the right both have the shape of a right triangle with 45\u00b0 angles, therefore they are similar in shape, while the middle ruler has 60\u00b0, 30\u00b0 angles.<\/p>\n<p><strong>STRUCTURE<\/strong><br \/>\n<strong>Tell whether the triangles are similar. Explain.<\/strong><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-110.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 110\" width=\"204\" height=\"100\" \/><\/p>\n<p>Answer:<br \/>\nm\u2220APB + m\u2220B = 90\u00b0<br \/>\nm\u2220APB + 51\u00b0 = 90\u00b0<br \/>\nm\u2220APB = 90\u00b0 &#8211; 51\u00b0<br \/>\nm\u2220APB = 39\u00b0<br \/>\nm\u2220APB + m\u2220BPD + m\u2220DPC = 180\u00b0<br \/>\n39\u00b0 + 102\u00b0 + m\u2220DPC = 180\u00b0<br \/>\nm\u2220DPC + 141\u00b0 = 180<br \/>\nm\u2220DPC = 180 &#8211; 141\u00b0<br \/>\nm\u2220DPC = 39\u00b0<br \/>\nm\u2220A = m\u2220C<br \/>\nm\u2220APB = m\u2220DPC<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-3-Angles-and-Triangles-111.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 3 Angles and Triangles 111\" width=\"251\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\n\u2220APB \u2245 \u2220CPD<br \/>\nm\u2220APB = m\u2220CPD<br \/>\nm\u2220APB = 29\u00b0<br \/>\nm\u2220A + m\u2220B + m\u2220APB = 180\u00b0<br \/>\nm\u2220A + 88\u00b0 + 29\u00b0 = 180\u00b0<br \/>\nm\u2220A\u00a0 + 117\u00b0 = 180\u00b0<br \/>\nm\u2220A = 180\u00b0 &#8211; 117\u00b0<br \/>\nm\u2220A = 63\u00b0<br \/>\nm\u2220PDC + m\u2220PDE = 180\u00b0<br \/>\nm\u2220PDC + 91\u00b0 = 180\u00b0<br \/>\nm\u2220PDC = 180\u00b0 &#8211; 91\u00b0<br \/>\nm\u2220PDC = 89\u00b0<\/p>\n<p><strong>IDENTIFYING SIMILAR TRIANGLES<\/strong><br \/>\n<strong>Can you determine whether the triangles are similar? Explain.<\/strong><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-112.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 112\" width=\"208\" height=\"134\" \/><\/p>\n<p>Answer:<br \/>\nPS || QR<br \/>\n\u2220PSQ and \u2220SQR are interior angles using the transversal QS, thus they are congruent.<br \/>\n\u2220PSQ \u2245 \u2220SQR<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-113.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 113\" width=\"185\" height=\"170\" \/><\/p>\n<p>Answer:<br \/>\nAs AB || DE there are two pairs of congruent alternate interior angles, using the transversals AE and BD.<br \/>\n\u2220A\u2245 \u2220E<br \/>\n\u2220B\u2245 \u2220D<br \/>\nThe two pairs of congruent angles are enough to prove that the triangles are similar.<br \/>\n\u0394ABC \u223c \u0394EDC<\/p>\n<p>Question 18.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA water sample must be taken from water atleast 20 feet deep. Find the depth of the water 50 feet from shore. Is this an appropriate location for a water sample?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-114.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 114\" width=\"278\" height=\"149\" \/><\/p>\n<p>Answer:<br \/>\n\u0394AMN \u223c \u0394ABC<br \/>\nMN\/BC = AM\/AB<br \/>\n1.5\/d = 5\/50<br \/>\nd = 1.5 \u00d7 10<br \/>\nd = 15 feet<br \/>\nTherefore 15 feet is not an appropriate location.<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA map shows the number of steps you must take to get to a treasure. However, the map is old, and the last dimension is unreadable. Explain why the triangles are similar. How many steps do you take from the pyramids to the treasure?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-115.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 115\" width=\"236\" height=\"213\" \/><\/p>\n<p>Answer:<br \/>\nThe two triangles are similar because they are right triangles and \u2220AXB \u2245 \u2220PXQ because they are vertical angles.<br \/>\nPQ\/300 = 80\/240<br \/>\n240PQ = 24000<br \/>\nPQ = 24000\/240<br \/>\nPQ = 100 steps<\/p>\n<p>Question 20.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA person who is 6 feet tall casts a 3-foot-long shadow. A nearby pine tree casts a 15-foot-long shadow. What is the height h of the pine tree?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-116.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 116\" width=\"234\" height=\"170\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA person who is 6 feet tall casts a 3-foot-long shadow.<br \/>\nA nearby pine tree casts a 15-foot-long shadow.<br \/>\n\u0394XAB \u223c \u0394XPQ<br \/>\nAB\/PQ = XB\/XQ<br \/>\n6\/PQ = 3\/15<br \/>\nPQ = 30 ft<\/p>\n<p>Question 21.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nYou place a mirror on the ground 6 feet from the lamppost. You move back 3 feet and see the top of the lamppost in the mirror. What is the height of the lamppost?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-54790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Grade-8-BIM-Chapter-3-Answer-Key-img_13-300x234.png\" alt=\"Grade 8 BIM Chapter 3 Answer Key img_13\" width=\"300\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Grade-8-BIM-Chapter-3-Answer-Key-img_13-300x234.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Grade-8-BIM-Chapter-3-Answer-Key-img_13.png 374w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\u0394XAB \u223c \u0394XPQ<br \/>\nAB\/PQ = XB\/XQ<br \/>\nh\/PQ = 6\/3<br \/>\nh = 2PQ<\/p>\n<p>Question 22.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIn each of two right triangles, one angle measure is two times another angle measure. Can you determine that the triangles are similar? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nWe are given the right triangle ABC<br \/>\nm\u2220A = 2m\u2220B<br \/>\nCase 1:<br \/>\nm\u2220A = 90\u00b0<br \/>\n90\u00b0 = 2m\u2220B<br \/>\nm\u2220B = 45\u00b0<br \/>\nm\u2220C = 180\u00b0 &#8211; 90\u00b0 &#8211; 45\u00b0 = 45\u00b0<br \/>\nCase 2:<br \/>\nm\u2220B = 90\u00b0<br \/>\nm\u2220A = 2 \u00d7 90\u00b0 = 180\u00b0<br \/>\nCase 3:<br \/>\nm\u2220C = 90\u00b0<br \/>\nm\u2220A + m\u2220B = 180 &#8211; m\u2220C = 180\u00b0 &#8211; 90\u00b0 = 90\u00b0<br \/>\n2m\u2220B + m\u2220B = 90\u00b0<br \/>\n3m\u2220B = 90\u00b0<br \/>\nm\u2220B = 30\u00b0<br \/>\nm\u2220A = 2 . 30\u00b0 = 60\u00b0<\/p>\n<p>Question 23.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nIn the diagram, \\(\\overline{B G}\\), \\(\\overline{C F}\\) and \\(\\overline{D E}\\) are parallel. The length of \\(\\overline{B D}\\) is 6.32 feet, and the length of \\(\\overline{D E}\\) is 6 feet. Name all pairs of similar triangles in the diagram. Then \ufb01nd the lengths of \\(\\overline{B G}\\) and \\(\\overline{C F}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-117.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 117\" width=\"288\" height=\"194\" \/><\/p>\n<p>Answer:<br \/>\n\u0394ABG \u223c \u0394ACF<br \/>\n\u0394ACF \u223c \u0394ADE<br \/>\n\u0394ABG \u223c \u0394ADE<br \/>\nAB = BC = CD = BD\/2 = 6.32\/2 = 3.16<br \/>\nAB\/CD = BG\/DE<br \/>\n3BG = 6<br \/>\nBG = 2 feet<br \/>\n\u0394ACF \u223c \u0394ADE<br \/>\nAC\/AD = CF\/DE<br \/>\n2\/3 = CF\/6<br \/>\n3CF = 2(6)<br \/>\nCF = 4 feet<\/p>\n<h3><a id=\"Angles_and_Triangles_Connecting_Concepts\"><\/a>Angles and Triangles Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nA dog park is divided into sections for large and small dogs. The ratio of the perimeter of the small dog section to the perimeter of the entire dog park is 7 : 12. Find the area of each section.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-118.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 118\" width=\"225\" height=\"163\" \/><\/p>\n<p><strong>Understand the problem<\/strong><br \/>\nYou know two dimensions of a dog park and the ratio of the perimeter of the small dog section to the perimeter of the entire park. You are asked to \ufb01nd the area of each section.<br \/>\n<strong>Make a plan<\/strong><br \/>\nVerify that the small triangle and the large triangle are similar. Then use the ratio of the perimeters to \ufb01nd the base or the height of each triangle and calculate the areas.<br \/>\n<strong>Solve and check.<\/strong><br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Answer:<\/p>\n<p>Question 2.<br \/>\nYou rotate lines m and t 180\u00b0 about point P. The image of line m is parallel to the original line. Use the diagram to show that when a transversal intersects parallel lines, each of the following pairs of angles are congruent. Explain your reasoning.<br \/>\na. alternate interior angles<br \/>\nb. alternate exterior angles<br \/>\nc. corresponding angles<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-119.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 119\" width=\"243\" height=\"126\" \/><\/p>\n<p>Answer:<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Turtle Shells<\/strong><\/p>\n<p>At the beginning of this chapter, you watched a STEAM Video called \u201cHoneycombs.\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-32104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-120.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 120\" width=\"282\" height=\"203\" \/><\/p>\n<h3><a id=\"Angles_and_Triangles_Chapter_Review\"><\/a>Angles and Triangles Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the de\ufb01nition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-121.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 121\" width=\"630\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-121.png 630w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-121-300x44.png 300w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><br \/>\nYou can use an Example and Non-Example to list examples and non-examples of a concept. Here is an Example and Non-Example Chart for transversals.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-122.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 122\" width=\"418\" height=\"387\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-122.png 418w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-122-300x278.png 300w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Choose and complete a graphic organizer to help you study the concept.<\/p>\n<ol>\n<li>interior angles formed by parallel lines and a transversal<\/li>\n<li>exterior angles formed by parallel lines and a transversal<\/li>\n<li>interior angles of a triangle<\/li>\n<li>exterior angles of a triangle<\/li>\n<li>polygons<\/li>\n<li>similar triangles<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-123.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 123\" width=\"314\" height=\"320\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-123.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-123-294x300.png 294w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/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-32108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-124.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 124\" width=\"642\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-124.png 642w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-124-300x40.png 300w\" sizes=\"(max-width: 642px) 100vw, 642px\" \/><\/p>\n<p><strong>3.1 Parallel Lines and Transversals<\/strong> (pp. 103\u2013110)<\/p>\n<p><strong>Use the \ufb01gure to \ufb01nd the measure of the angle. Explain your reasoning.<\/strong><\/p>\n<p>Question 1.<br \/>\n\u22208<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-125.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 125\" width=\"237\" height=\"130\" \/><\/p>\n<p>Answer: 140\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22208 and 140 degrees angle are alternate exterior angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22208 is 140\u00b0<\/p>\n<p>Question 2.<br \/>\n\u22205<\/p>\n<p>Answer: 140\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22205 and 140 degrees angle are corresponding angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22205 is 140\u00b0<\/p>\n<p>Question 3.<br \/>\n\u22207<\/p>\n<p>Answer: 40\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22205 and 140 degrees angle are corresponding angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22205 is 140\u00b0<br \/>\n\u22205 and \u22207 are supplementary angle.<br \/>\n\u22205 + \u22207 = 180\u00b0<br \/>\n140\u00b0 + \u22207 = 180\u00b0<br \/>\n\u22207 = 180\u00b0 &#8211; 140\u00b0<br \/>\n\u22207 = 40\u00b0<br \/>\nSo, the measure of \u22207 is 40\u00b0<\/p>\n<p>Question 4.<br \/>\n\u22202<\/p>\n<p>Answer: 40\u00b0<\/p>\n<p>Explanation:<br \/>\n140 and \u22202 are supplementary angle.<br \/>\n140\u00b0 + \u22202 = 180\u00b0<br \/>\n\u22202 = 180\u00b0 &#8211; 140\u00b0<br \/>\n\u22202 = 40\u00b0<br \/>\nSo, the measure of \u22202 is 40\u00b0<\/p>\n<p>Question 5.<br \/>\n\u22206<\/p>\n<p>Answer: 40\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22205 and 140 degrees angle are corresponding angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22205 is 140\u00b0<br \/>\n\u22205 and \u22206 are supplementary angle.<br \/>\n140\u00b0 + \u22206 = 180\u00b0<br \/>\n\u22206 = 180\u00b0 &#8211; 140\u00b0<br \/>\n\u22206 = 40\u00b0<br \/>\nSo, the measure of \u22206 is 40\u00b0<\/p>\n<p><strong>Complete the statement. Explain your reasoning.<\/strong><\/p>\n<p>Question 6.<br \/>\nIf the measure of \u22201 = 123\u00b0, then the measure of \u22207 = <img loading=\"lazy\" class=\"alignnone size-full wp-image-32110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-126.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 126\" width=\"85\" height=\"38\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-127.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 127\" width=\"185\" height=\"129\" \/><\/p>\n<p>Answer: 123\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22201 and \u22207 are alternate exterior angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22207 is 123\u00b0<\/p>\n<p>Question 7.<br \/>\nIf the measure of \u22202 = 58\u00b0, then the measure of <img loading=\"lazy\" class=\"alignnone size-full wp-image-32111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-127.1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 127.1\" width=\"85\" height=\"40\" \/><\/p>\n<p>Answer: 122\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22202 and \u22206 are corresponding angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22206 is 58\u00b0<br \/>\n\u22205 and \u22206 are supplementary angle.<br \/>\n\u22205 + \u22206 = 180\u00b0<br \/>\n58\u00b0 + \u22205 = 180\u00b0<br \/>\n\u22205 = 180\u00b0 &#8211; 58\u00b0<br \/>\n\u22205 = 122\u00b0<br \/>\nSo, the measure of \u22205 is 122\u00b0<\/p>\n<p>Question 8.<br \/>\nIf the measure of \u22205 = 119\u00b0, then the measure of <img loading=\"lazy\" class=\"alignnone size-full wp-image-32113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-128.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 128\" width=\"86\" height=\"39\" \/><\/p>\n<p>Answer: 119\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22203 and \u22205 are alternate interior angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22203 is 119\u00b0<\/p>\n<p>Question 9.<br \/>\nIf the measure of \u22204 = 60\u00b0, then the measure of <img loading=\"lazy\" class=\"alignnone size-full wp-image-32116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-129.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 129\" width=\"90\" height=\"41\" \/><\/p>\n<p>Answer: 60\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22204 and \u22206 are alternate exterior angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nSo, the measure of \u22204 is 60\u00b0<\/p>\n<p>Question 10.<br \/>\nIn Exercises 6\u20139, describe the relationship between \u22202 and \u22208.<\/p>\n<p>Answer: \u22202 \u2245 \u22208<\/p>\n<p>Question 11.<br \/>\nIn a park, a bike path and a horse riding path are parallel. In one part of the park, a hiking trail intersects the two paths. Find the measures of \u22201 and \u22202. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-129.1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 129.1\" width=\"223\" height=\"161\" \/><\/p>\n<p>Answer: \u22201 = 108\u00b0, \u22202 = 108\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22203 and 72\u00b0 are alternate interior angles. They are congruent.<br \/>\nSo, the measure of \u22203 is 72\u00b0<br \/>\n\u22203 + \u22201 = 180\u00b0<br \/>\n72\u00b0 + \u22201 = 180\u00b0<br \/>\n\u22201 = 180\u00b0 &#8211; 72\u00b0<br \/>\n\u22201 = 108\u00b0<br \/>\nSo, the measure of \u22201 is 108\u00b0<br \/>\n\u22201 and \u22202 are alternating interior angles. They are congruent.<\/p>\n<p><strong>3.2 Angles of Triangles (pp. 111 &#8211; 116)<\/strong><\/p>\n<p><strong>Find the measures of the interior angles of the triangle.<\/strong><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-129.2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 129.2\" width=\"142\" height=\"135\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + 50\u00b0 + 55\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 105\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 105\u00b0<br \/>\nx\u00b0 = 75\u00b0<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-130.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 130\" width=\"195\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + (x + 8)\u00b0 + 90\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + 8\u00b0 + 90\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + 98\u00b0 = 180\u00b0<br \/>\n2x\u00b0 = 180\u00b0 &#8211; 98\u00b0<br \/>\n2x\u00b0 = 82<br \/>\nx\u00b0 = 82\/2<br \/>\nx\u00b0 = 41\u00b0<br \/>\n(x + 8)\u00b0 = (41 + 8)\u00b0 = 49\u00b0<\/p>\n<p><strong>Find the measure of the exterior angle.<\/strong><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-131.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 131\" width=\"214\" height=\"103\" \/><\/p>\n<p>Answer:<br \/>\ns\u00b0 = 50\u00b0 + 75\u00b0<br \/>\ns\u00b0 = 125\u00b0<br \/>\nThus the measure of the exterior angle is 125\u00b0<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-132.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 132\" width=\"178\" height=\"137\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nt\u00b0 + (t + 10)\u00b0 + (t + 20)\u00b0 = 180\u00b0<br \/>\n3t\u00b0 + 10\u00b0 + 20\u00b0 = 180\u00b0<br \/>\n3t\u00b0 + 30\u00b0 = 180\u00b0<br \/>\n3t\u00b0 = 180\u00b0 &#8211; 30\u00b0<br \/>\n3t\u00b0 = 150\u00b0<br \/>\nt\u00b0 = 150\/3<br \/>\nt\u00b0 = 50\u00b0<br \/>\nExterior angle:<br \/>\nt\u00b0 + (t + 10)\u00b0<br \/>\nt\u00b0 + t\u00b0 + 10\u00b0<br \/>\n2t\u00b0 + 10\u00b0<br \/>\n2(50)\u00b0 + 10\u00b0<br \/>\n= 100\u00b0 + 10\u00b0<br \/>\n= 110\u00b0<br \/>\nThus the measure of the exterior angle is 110\u00b0.<\/p>\n<p>Question 16.<br \/>\nWhat is the measure of each interior angle of an equilateral triangle? Explain.<\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (3- 2) . 180\u00b0<br \/>\nS = 1 . 180\u00b0<br \/>\nS = 180\u00b0<br \/>\nThus the sum of the interior angle measure is 180\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 3.<br \/>\n180 \u00f7 3 = 60\u00b0<\/p>\n<p>Question 17.<br \/>\nYou draw the Leo constellation. You notice that the three stars Denebola, Zosma, and Chertan form a triangle. In your drawing, you \ufb01nd the measure of the interior angle at Denebola is 30\u00b0 and the measure of the interior angle of the triangle at Zosma is 56\u00b0. What is the measure of the interior angle of the triangle at Chertan?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-133.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 133\" width=\"210\" height=\"227\" \/><\/p>\n<p>Answer:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + 30\u00b0 + 56\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 86\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 86\u00b0<br \/>\nx\u00b0 = 94\u00b0<br \/>\nThus the measure of the interior angle of the triangle at Chertan = 94\u00b0<\/p>\n<p><strong>3.3 Angles of Polygons<\/strong> (pp. 117\u2013122)<\/p>\n<p><strong>Find the sum of the interior angle measures of the polygon.<\/strong><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-134.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 134\" width=\"118\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nThe polygon has 13 sides<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (13- 2) . 180\u00b0<br \/>\nS = 11 . 180\u00b0<br \/>\nS = 1980\u00b0<br \/>\nThus the sum of the interior angle measure is 1980\u00b0<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-135.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 135\" width=\"140\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nThe polygon has 9 sides<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (9- 2) . 180\u00b0<br \/>\nS = 7 . 180\u00b0<br \/>\nS = 1260\u00b0<br \/>\nThus the sum of the interior angle measure is 1260\u00b0<\/p>\n<p><strong>Find the value of x.<\/strong><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-136.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 136\" width=\"154\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (4 &#8211; 2) . 180\u00b0<br \/>\nS = 2 . 180\u00b0<br \/>\nS = 360\u00b0<br \/>\nThus the sum of the interior angle measure is 360\u00b0<br \/>\nx\u00b0 + 60\u00b0 + 128\u00b0 + 95\u00b0 = 360\u00b0<br \/>\nx\u00b0 + 283\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\u00b0 &#8211; 283\u00b0<br \/>\nx\u00b0 = 77\u00b0<br \/>\nThus the value of x is 77\u00b0.<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-137.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 137\" width=\"149\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (7 &#8211; 2) . 180\u00b0<br \/>\nS = 5 . 180\u00b0<br \/>\nS = 900\u00b0<br \/>\nThus the sum of the interior angle measure is 900\u00b0<br \/>\nx\u00b0 + 135\u00b0 + 125\u00b0 + 135\u00b0 + 105\u00b0 + 150\u00b0 + 140\u00b0 = 900\u00b0<br \/>\nx\u00b0 + 790\u00b0 = 900\u00b0<br \/>\nx\u00b0 = 900\u00b0 &#8211; 790\u00b0<br \/>\nx\u00b0 = 110\u00b0<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-138.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 138\" width=\"144\" height=\"149\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (6 &#8211; 2) . 180\u00b0<br \/>\nS = 4 . 180\u00b0<br \/>\nS = 720\u00b0<br \/>\nThus the sum of the interior angle measure is 720\u00b0<br \/>\nx\u00b0 + 120\u00b0 + 140\u00b0 + 92\u00b0 + 125\u00b0 + 130\u00b0 = 720\u00b0<br \/>\nx\u00b0 + 607\u00b0 = 720\u00b0<br \/>\nx\u00b0 = 720\u00b0 &#8211; 607\u00b0<br \/>\nx\u00b0 = 113\u00b0<br \/>\nThe value of x\u00b0 is 113\u00b0<\/p>\n<p>Question 23.<br \/>\nFind the measure of each interior angle of the regular polygon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-139.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 139\" width=\"142\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nThe given polygon is an octagon. It has 8 sides.<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (8 &#8211; 2) . 180\u00b0<br \/>\nS = 6 . 180\u00b0<br \/>\nS = 1080\u00b0<br \/>\nThus the sum of the interior angle measure is 1080\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 8.<br \/>\n1080 \u00f7 3 = 135\u00b0<\/p>\n<p><strong>3.4 Using Similar Triangles (pp. 123\u2013128)<\/strong><\/p>\n<p><strong>Tell whether the triangles are similar. Explain.<\/strong><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-140.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 140\" width=\"181\" height=\"157\" \/><\/p>\n<p>Answer:<br \/>\nx\u00b0 + 68\u00b0 + 90\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 158\u00b0<br \/>\nx\u00b0 = 22\u00b0<br \/>\ny\u00b0 + 22\u00b0 + 90\u00b0 = 180\u00b0<br \/>\ny\u00b0 + 112\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 112\u00b0<br \/>\ny\u00b0 = 68\u00b0<br \/>\nThe triangles have two pairs of congruent angles.<br \/>\nSo, the triangles are similar.<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-141.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 141\" width=\"224\" height=\"180\" \/><\/p>\n<p>Answer:<br \/>\nx\u00b0 + 100\u00b0 + 30\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 130\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 130\u00b0<br \/>\nx\u00b0 = 50\u00b0<br \/>\ny\u00b0 + 100\u00b0 + 50\u00b0 = 180\u00b0<br \/>\ny\u00b0 + 150\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 150\u00b0<br \/>\ny\u00b0 = 30\u00b0<br \/>\nThe triangles have two pairs of congruent angles.<br \/>\nSo, the triangles are similar.<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-142.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 142\" width=\"198\" height=\"193\" \/><\/p>\n<p>Answer:<br \/>\nx\u00b0 + 50\u00b0 + 85\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 135\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 135\u00b0<br \/>\nx\u00b0 = 45\u00b0<br \/>\ny\u00b0 + 85\u00b0 + 35\u00b0 = 180\u00b0<br \/>\ny\u00b0 + 120\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 120\u00b0<br \/>\ny\u00b0 = 60\u00b0<br \/>\nThe triangles do not have two pairs of congruent angles.<br \/>\nSo, the triangles are not similar.<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-143.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 143\" width=\"165\" height=\"197\" \/><\/p>\n<p>Answer:<br \/>\n\u2220B \u2245 \u2220D<br \/>\n\u2220A \u2245 \u2220C<br \/>\n\u2220AXB \u2245 \u2220CXD<br \/>\n\u2220AXB and \u2220CXD are vertical angles.<br \/>\n\u0394AXB \u223c \u0394CXD<\/p>\n<p>Question 28.<br \/>\nA person who is 5 feet tall casts a shadow that is 4 feet long. A nearby building casts a shadow that is 24 feet long. What is the height of the building?<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA person who is 5 feet tall casts a shadow that is 4 feet long.<br \/>\nA nearby building casts a shadow that is 24 feet long.<br \/>\nLet the height of the building = x ft<br \/>\nx\/24 = 5\/4<br \/>\n24 . x\/24 = 5\/4 . 24<br \/>\nx = 30<br \/>\nThus the height of the building is 30 ft.<\/p>\n<h3><a id=\"Angles_and_Triangles_Practice_Test\"><\/a>Angles and Triangles Practice Test<\/h3>\n<p><strong>Practice Test<\/strong><\/p>\n<p>Use the \ufb01gure to \ufb01nd the measure of the angle. Explain your reasoning.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-144.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 144\" width=\"241\" height=\"119\" \/><\/p>\n<p>Question 1.<br \/>\n\u22207<\/p>\n<p>Answer: 47\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22207 and 47\u00b0 angles are alternate exterior angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nThus the measure of \u22207 is 47\u00b0<\/p>\n<p>Question 2.<br \/>\n\u22206<\/p>\n<p>Answer: 47\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22206 and 47\u00b0 angles are corresponding angles formed by a transversal intersecting parallel lines. The angles are congruent.<br \/>\nThus the measure of \u22206 is 47\u00b0<\/p>\n<p>Question 3.<br \/>\n\u22204<\/p>\n<p>Answer: 133\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22204 and 47\u00b0 are supplementary angles.<br \/>\n47\u00b0 + \u22204 = 180\u00b0<br \/>\n\u22204 = 180\u00b0 &#8211; 47\u00b0<br \/>\n\u22204 = 133\u00b0<br \/>\nThus the measure of \u22204 = 133\u00b0<\/p>\n<p>Question 4.<br \/>\n\u22205<\/p>\n<p>Answer: 133\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22206 and 47\u00b0 angles are corresponding angles formed by transversal intersecting parallel lines. The angles are congruent.<br \/>\nThus the measure of \u22206 is 47\u00b0<br \/>\n\u22206 + \u22205 = 180\u00b0<br \/>\n47\u00b0 + \u22205 = 180\u00b0<br \/>\n\u22205 = 180\u00b0 &#8211; 47\u00b0<br \/>\n\u22205 = 133\u00b0<br \/>\nThus the measure of \u22205 = 133\u00b0<\/p>\n<p>Question 5.<br \/>\nFind the value of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-144.1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 144.1\" width=\"194\" height=\"84\" \/><\/p>\n<p>Answer: 28\u00b0<\/p>\n<p>Explanation:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + 129\u00b0 + 23\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 152\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 152\u00b0<br \/>\nx\u00b0 = 28\u00b0<br \/>\nThus the value of x\u00b0 is 28\u00b0<\/p>\n<p>Question 6.<br \/>\nFind the measures of the interior angles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-145.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 145\" width=\"137\" height=\"91\" \/><\/p>\n<p>Answer: 68\u00b0<\/p>\n<p>Explanation:<br \/>\nSum of all the angles in a triangle = 180\u00b0<br \/>\nx\u00b0 + (x &#8211; 24)\u00b0 + 68\u00b0 = 180\u00b0<br \/>\nx\u00b0 + x\u00b0 &#8211; 24\u00b0 + 68\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + 44\u00b0 = 180\u00b0<br \/>\n2x\u00b0 = 180\u00b0 &#8211; 44\u00b0<br \/>\n2x\u00b0 = 136\u00b0<br \/>\nx\u00b0 = 68\u00b0<br \/>\n(x &#8211; 24)\u00b0 = (68 &#8211; 24)\u00b0 = 44\u00b0<\/p>\n<p>Question 7.<br \/>\nFind the measure of the exterior angle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-146.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 146\" width=\"245\" height=\"100\" \/><\/p>\n<p>Answer:<br \/>\nj\u00b0 = 40\u00b0 + 90\u00b0<br \/>\nj\u00b0 = 130\u00b0<br \/>\nThe measure of an exterior angle is 130\u00b0.<\/p>\n<p>Question 8.<br \/>\nFind the measure of the interior angle measures of the border of the coin.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-147.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 147\" width=\"132\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nThe coin has 7 sides.<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (7 &#8211; 2) . 180\u00b0<br \/>\nS = 5 . 180\u00b0<br \/>\nS = 900\u00b0<br \/>\nThus the sum of the interior angle measure is 900\u00b0<\/p>\n<p>Question 9.<br \/>\nFind the value of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-148.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 148\" width=\"155\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (5 &#8211; 2) . 180\u00b0<br \/>\nS = 3 . 180\u00b0<br \/>\nS = 540\u00b0<br \/>\nThus the sum of the interior angle measure is 540\u00b0<br \/>\n2x\u00b0 + 125\u00b0 + 90\u00b0 + 2x\u00b0 + 125\u00b0 = 540\u00b0<br \/>\n4x\u00b0 + 340\u00b0 = 540\u00b0<br \/>\n4x\u00b0 = 540\u00b0 &#8211; 340\u00b0<br \/>\n4x\u00b0 = 200\u00b0<br \/>\nx\u00b0 = 200\/4<br \/>\nx\u00b0 = 50\u00b0<br \/>\nThe value of x\u00b0 is 50\u00b0<\/p>\n<p>Question 10.<br \/>\nFind the measure of each interior angle of the regular polygon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-149.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 149\" width=\"117\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (6 &#8211; 2) . 180\u00b0<br \/>\nS = 4 . 180\u00b0<br \/>\nS = 720\u00b0<br \/>\nThus the sum of the interior angle measure is 720\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 6.<br \/>\n720 \u00f7 6 = 120\u00b0<\/p>\n<p><strong>Tell whether the triangles are similar. Explain.<\/strong><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-150.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 150\" width=\"264\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nTo find x\u00b0:<br \/>\nx\u00b0 + 61\u00b0 + 70\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 131\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 131\u00b0<br \/>\nx\u00b0 = 49\u00b0<br \/>\nTo find y\u00b0:<br \/>\nx\u00b0 + 39\u00b0 + 70\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 109\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 109\u00b0<br \/>\nx\u00b0 = 71\u00b0<br \/>\nThe triangles do not have two pairs of congruent angles.<br \/>\nSo, the triangles are not similar.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-151.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 151\" width=\"185\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\n\u2220A \u2245 \u2220QPB<br \/>\n\u2220C \u2245 \u2220PQB<br \/>\n\u0394BPQ \u223c \u0394BAC<\/p>\n<p>Question 13.<br \/>\nDescribe two ways you can \ufb01nd the measure of \u22205.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-3-Angles-and-Triangles-152.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles 152\" width=\"239\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nOne way: \u22203 and 65\u00b0 are supplementary angles. \u22205 and \u22203 are alternate interior angles.<br \/>\nAnother way: \u22208 and 65\u00b0 are alternate exterior angles. \u22205 and \u22208 are supplementary angles.<\/p>\n<p>Question 14.<br \/>\nYou swim 3.6 kilometers per hour. How long (in minutes) will it take you to swim the distance d across the pond?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-153.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 153\" width=\"243\" height=\"156\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nYou swim 3.6 kilometers per hour.<br \/>\nd\/105 = 80\/140<br \/>\n105 . d\/105 = 80\/140 . 105<br \/>\nd = 60<br \/>\nThe length of the pond is 60 m.<br \/>\nSpeed = 3.6 km per hour = 1 m sec<br \/>\nDistance = d = 60m<br \/>\nTime it will take to swim across the pond<br \/>\n= distance\/speed<br \/>\n= 60\/1<br \/>\n= 60 sec = 1 min<\/p>\n<h3><a id=\"Angles_and_Triangles_Cumulative_Practice\"><\/a>Angles and Triangles Cumulative Practice<\/h3>\n<p>Question 1.<br \/>\nThe border of a Canadian one-dollar coin is shaped like an 11-sided regular polygon. The shape was chosen to help visually impaired people identify the coin. How many degrees are in each interior angle along the border? Round your answer to the nearest degree.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-154.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 154\" width=\"76\" height=\"68\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-154.1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 154.1\" width=\"350\" height=\"385\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-154.1.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-154.1-273x300.png 273w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (11 &#8211; 2) . 180\u00b0<br \/>\nS = 9 . 180\u00b0<br \/>\nS = 1620\u00b0<br \/>\nThus the sum of the interior angle measure is 1620\u00b0<br \/>\nIn a regular polygon, each interior angle is congruent. So, divide the sum of the interior angle measures by the number of interior angles, 11.<br \/>\n1620 \u00f7 11 = 147\u00b0<\/p>\n<p>Question 2.<br \/>\nA public utility charges its residential customers for natural gas based on the number of therms used each month. The formula shows how the monthly cost tin dollars is related to the number of terms used.<br \/>\nC = 11 + 1.6t<br \/>\nSolve this formula for t.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-155.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 155\" width=\"460\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-155.png 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-155-300x57.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/p>\n<p>Answer:<br \/>\nC = 11 + 1.6t<br \/>\nC &#8211; 11 = 1.6t<br \/>\n1.6t = C &#8211; 11<br \/>\nt = (C &#8211; 11)\/1.6<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 3.<br \/>\nWhat is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-156.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 156\" width=\"398\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-156.png 398w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-156-300x99.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p>\n<p>Answer:<br \/>\n5(x &#8211; 4) = 3x<br \/>\n5x &#8211; 20 = 3x<br \/>\n5x &#8211; 3x = 20<br \/>\n2x = 20<br \/>\nx = 20\/2<br \/>\nx = 10<br \/>\nThus the correct answer is option I.<\/p>\n<p>Question 4.<br \/>\nIn the \ufb01gures, \u25b3PQR is similar to \u25b3STU. What is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-157.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 157\" width=\"309\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-157.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-157-300x152.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nA. 9.6<br \/>\nB. 10\\(\\frac{2}{3}\\)<br \/>\nC. 13.5<br \/>\nD. 15<\/p>\n<p>Answer:<br \/>\n\u25b3PQR is similar to \u25b3STU<br \/>\nPQ = 12<br \/>\nST = 16<br \/>\nSU = 20<br \/>\nTU = 18<br \/>\nPQ\/ST = QR\/TU<br \/>\n12\/16 = X\/18<br \/>\n16X = 12 \u00d7 18<br \/>\nX = 216\/16<br \/>\nX = 13.5 cm<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 5.<br \/>\nWhat is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-158.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 158\" width=\"598\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-158.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-158-300x153.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Answer:<br \/>\n\u2220y and 125\u00b0 are supplementary angles.<br \/>\n125\u00b0 + \u2220y = 180\u00b0<br \/>\n\u2220y = 180\u00b0 &#8211; 125\u00b0<br \/>\n\u2220y = 55\u00b0<br \/>\nSo, the measure of \u2220y = 55\u00b0<br \/>\n\u2220x and \u2220y are alternate interior angles. They are congruent.<br \/>\nSo, the measure of \u2220x = 55\u00b0<\/p>\n<p>Question 6.<br \/>\nYour friend was solving an equation in the box shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-159.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 159\" width=\"257\" height=\"299\" \/><br \/>\nWhat should your friend do to correct the error that she made?<br \/>\nF. Multiply both sides by &#8211;\\(\\frac{5}{2}\\) instead of &#8211;\\(\\frac{2}{5}\\).<br \/>\nG. Multiply both sides by \\(\\frac{2}{5}\\) instead of &#8211;\\(\\frac{2}{5}\\).<br \/>\nH. Distribute &#8211;\\(\\frac{2}{5}\\) to get 4x &#8211; 6.<br \/>\nI. Add 15 to -30.<\/p>\n<p>Answer:<br \/>\nMy friend made the error by multiplying both sides by &#8211;\\(\\frac{2}{5}\\).<br \/>\nTo correct the error she should multiply both sides by &#8211;\\(\\frac{5}{2}\\) instead of &#8211;\\(\\frac{2}{5}\\)<br \/>\nThus the correct answer is option F.<\/p>\n<p>Question 7.<br \/>\nIn the coordinate plane below, \u2206XYZ is plotted and its vertices are labeled.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-160.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 160\" width=\"205\" height=\"163\" \/><br \/>\nWhich of the following shows \u2206X&#8217;Y&#8217;Z&#8217;, the image of \u2206XYZ after it is re\ufb02ected in the y-axis?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-161.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 161\" width=\"558\" height=\"337\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-161.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-161-300x181.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nX(-6,-1)<br \/>\nY(-3,-5)<br \/>\nX(-2,-3)<br \/>\nReflecting a point (x,y) in the y-axis.<br \/>\n(x, y) = (-x, y)<br \/>\nX(-6,-1) = X'(6, -1)<br \/>\nY(-3,-5) = Y'(3, -5)<br \/>\nX(-2,-3) = Z'(2, -3)<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 8.<br \/>\nThe sum S of the interior angle measures of a polygon with n sides can be found by using a formula.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-162.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 162\" width=\"76\" height=\"90\" \/><br \/>\n<strong>Part A<\/strong><br \/>\nWrite the formula.<\/p>\n<p>Answer:<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\n<strong>Part B<\/strong><br \/>\nA quadrilateral has angles measuring 100\u00b0, 90\u00b0, and 90\u00b0. Find the measure of its fourth angle. Show your work and explain your reasoning.<\/p>\n<p>Answer:<br \/>\nThe quadrilateral has 4 sides<br \/>\nS = (n &#8211; 2) . 180\u00b0<br \/>\nS = (4 &#8211; 2) . 180\u00b0<br \/>\nS = 2 . 180\u00b0<br \/>\nS = 360 \u00b0<br \/>\nThus the sum of the interior angles is 360 \u00b0<br \/>\nx\u00b0 + 100\u00b0 + 90\u00b0 + 90\u00b0 = 360\u00b0<br \/>\nx\u00b0 + 280\u00b0 = 360\u00b0<br \/>\nx\u00b0 = 360\u00b0 &#8211; 280\u00b0<br \/>\nx\u00b0 = 80\u00b0<br \/>\nThus the value of x\u00b0 is 80\u00b0<\/p>\n<p>Part C<br \/>\nThe sum of the measures of the angles of the pentagon shown is 540\u00b0. Divide the pentagon into triangles to show why this must be true. Show your work and explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-3-Angles-and-Triangles-163.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 3 Angles and Triangles 163\" width=\"185\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nNumber of sides = 3<br \/>\nThe number of interior triangles in the given figure = 3<br \/>\nSum of the interior angles measure using triangle = 3 \u00d7 180\u00b0 = 540<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>I wish the details prevailed in the above article is beneficial for all the 8th grade students. Hope our Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles helped you a lot to overcome the difficulties in this chapter. Feel free to post your comments in the comment box. Stay tuned to our ccssmathanswers.com to get step by step explanation for all the Grade 8 chapters.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Middle School Students who are struggling with the concepts of Big Ideas Math Grade 8 Ch 3 Angles and Triangles need not worry anymore. Big Ideas Math Book 8th Grade Chapter 3 Angles and Triangles help you finish your homework in time and gives you assistance whenever you need it. Detailed Solutions provided in Big &#8230; <a title=\"Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-3\/\" aria-label=\"More on Big Ideas Math Answers Grade 8 Chapter 3 Angles and Triangles\">Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":89232,"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\/02\/Big-Ideas-Math-Answers-Grade-8-Chapter-3.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/31930"}],"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=31930"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/31930\/revisions"}],"predecessor-version":[{"id":90352,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/31930\/revisions\/90352"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89232"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=31930"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=31930"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=31930"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}