{"id":6737,"date":"2022-03-25T21:24:20","date_gmt":"2022-03-25T15:54:20","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=6737"},"modified":"2022-04-07T12:45:40","modified_gmt":"2022-04-07T07:15:40","slug":"go-math-grade-8-answer-key-chapter-11-angle-relationships-in-parallel-lines-and-triangles","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-11-angle-relationships-in-parallel-lines-and-triangles\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles"},"content":{"rendered":"<p>Are you browsing for Go Math Grade 8 Answer Key for Chapter 11 Angle Relationships in Parallel Lines and Triangles on the various websites? Don&#8217;t worry discover all the questions, answers, and explanations on Go Math Grade 8 Solution Key Ch 11 Angle Relationships in Parallel Lines and Triangles here. Get free access to Download Go Math Grade 8 Chapter 11 Angle Relationships in Parallel Lines and Triangles Solution Key PDF from this page. Finish your homework in time with the help of <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-8-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 8 Answer Key<\/a>.<\/p>\n<h2>Download Go Math Grade 8 Chapter 11 Angle Relationships in Parallel Lines and Triangles Answer Key PDF<\/h2>\n<p>Enhance your skills by using the Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles. Download Go Math Grade 8 Chapter 11 Answer Key and go through Questions and Answers on our website. Follow the below given Go Math Grade 8 Chapter 11 Angle Relationships in Parallel Lines and Triangles Answer Key topic wise links and start your preparation. Make use of the links and secure a good percentage in the exam.<\/p>\n<p><strong>Lesson 1: Parallel Lines Cut by a Transversal<\/strong><\/p>\n<ul>\n<li><a href=\"#Parallel_Lines_Cut_by_a_Transversal_\u2013_Page_No._350\">Parallel Lines Cut by a Transversal \u2013 Page No. 350<\/a><\/li>\n<li><a href=\"#Parallel_Lines_Cut_by_a_Transversal_\u2013_Page_No._351\">Parallel Lines Cut by a Transversal \u2013 Page No. 351<\/a><\/li>\n<li><a href=\"#Parallel_Lines_Cut_by_a_Transversal_Lesson_Check_\u2013_Page_No._352\">Parallel Lines Cut by a Transversal Lesson Check \u2013 Page No. 352<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Angle Theorems for Triangles<\/strong><\/p>\n<ul>\n<li><a href=\"#Angle_Theorems_for_Triangles_\u2013_Page_No._358\">Angle Theorems for Triangles \u2013 Page No. 358<\/a><\/li>\n<li><a href=\"#Angle_Theorems_for_Triangles_\u2013_Page_No._359\">Angle Theorems for Triangles \u2013 Page No. 359<\/a><\/li>\n<li><a href=\"#Angle_Theorems_for_Triangles_Lesson_Check_\u2013_Page_No._360\">Angle Theorems for Triangles Lesson Check \u2013 Page No. 360<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Angle-Angle Similarity<\/strong><\/p>\n<ul>\n<li><a href=\"#Angle-Angle_Similarity_\u2013_Page_No._366\">Angle-Angle Similarity \u2013 Page No. 366<\/a><\/li>\n<li><a href=\"#Angle-Angle_Similarity_\u2013_Page_No._367\">Angle-Angle Similarity \u2013 Page No. 367<\/a><\/li>\n<li><a href=\"#Angle-Angle_Similarity_Lesson_Check_\u2013_Page_No._368\">Angle-Angle Similarity Lesson Check \u2013 Page No. 368<\/a><\/li>\n<\/ul>\n<p><strong>Model Quiz<\/strong><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><a href=\"#Model_Quiz_\u2013_Page_No._369\">Model Quiz \u2013 Page No. 369<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Review<\/strong><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><a href=\"#Mixed_Review_\u2013_Page_No._370\">Mixed Review \u2013 Page No. 370<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><a id=\"Parallel_Lines_Cut_by_a_Transversal_\u2013_Page_No._350\"><\/a>Guided Practice &#8211; Parallel Lines Cut by a Transversal &#8211; Page No. 350<\/h3>\n<p><strong>Use the figure for Exercises 1\u20134.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 1: Parallel Lines Cut by a Transversal img 1\" width=\"254\" height=\"198\" \/><\/p>\n<p>Question 1.<br \/>\n\u2220UVY and ____ are a pair of corresponding angles.<br \/>\n\u2220 _________<\/p>\n<p>Answer:<br \/>\n\u2220 VWZ<\/p>\n<p>Explanation:<br \/>\n\u2220UVY and \u2220 VWZ are a pair of corresponding angles.<br \/>\nWhen two lines are crossed by Transversal the angles in matching corners are called corresponding angles.<\/p>\n<p>Question 2.<br \/>\n\u2220WVY and \u2220VWT are _________ angles.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n\u2220WVY and \u2220VWT are alternate interior angles.<br \/>\nAlternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.<\/p>\n<p>Explanation:<br \/>\n\u2220WVY and \u2220VWT are alternate interior angles.<br \/>\nAlternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.<\/p>\n<p>Question 3.<br \/>\nFind m\u2220SVW.<br \/>\n_________ \u00b0<\/p>\n<p>Answer:<br \/>\n80\u00ba<\/p>\n<p>Explanation:<br \/>\n\u2220SVW and \u2220VWT are same sider interior angles. Therefore,<br \/>\nm\u2220SVW + m\u2220VWT = 180\u00ba<br \/>\n4x\u00ba +5x\u00ba = 180\u00ba<br \/>\n9x = 180\u00ba<br \/>\nx = 180\/9<br \/>\nx = 20<br \/>\nm\u2220SVW = 4x\u00ba = (4.20)\u00ba = 80\u00ba<\/p>\n<p>Question 4.<br \/>\nFind m\u2220VWT.<br \/>\n_________ \u00b0<\/p>\n<p>Answer:<br \/>\n100\u00ba<\/p>\n<p>Explanation:<br \/>\n\u2220SVW and \u2220VWT are same sider interior angles. Therefore,<br \/>\nm\u2220SVW + m\u2220VWT = 180\u00ba<br \/>\n4x\u00ba +5x\u00ba = 180\u00ba<br \/>\n9x = 180\u00ba<br \/>\nx = 180\/9<br \/>\nx = 20<br \/>\nm\u2220VWT = 5x\u00ba = (5.20)\u00ba = 100\u00ba<\/p>\n<p>Question 5.<br \/>\nVocabulary When two parallel lines are cut by a transversal, _______________ angles are supplementary.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nIf two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 6.<br \/>\nWhat can you conclude about the interior angles formed when two parallel lines are cut by a transversal?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAlternate interior angles are congruent; same-side interior angles are supplementary.<\/p>\n<p>Explanation:<br \/>\nWhen two parallel lines are cut by a transversal, the interior angles will be the angles between the two parallel lines. Alternate interior angles will be on opposite sides of the transversal; the measures of these angles are the same.<br \/>\nSame-side interior angles will be on the same side of the transversal; the measures of these angles will be supplementary, adding up to 180 degrees.<\/p>\n<h3><a id=\"Parallel_Lines_Cut_by_a_Transversal_\u2013_Page_No._351\"><\/a>11.1 Independent Practice &#8211; Parallel Lines Cut by a Transversal &#8211; Page No. 351<\/h3>\n<p><strong>Vocabulary Use the figure for Exercises 7\u201310.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 1: Parallel Lines Cut by a Transversal img 2\" width=\"173\" height=\"269\" \/><\/p>\n<p>Question 7.<br \/>\nName all pairs of corresponding angles.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n\u22201 and \u22205<br \/>\n\u22203 and \u22207<br \/>\n\u22202 and \u22206<br \/>\n\u22204 and \u22208<\/p>\n<p>Explanation:<br \/>\nCorresponding angles are<br \/>\n\u22201 and \u22205<br \/>\n\u22203 and \u22207<br \/>\n\u22202 and \u22206<br \/>\n\u22204 and \u22208<\/p>\n<p>Question 8.<br \/>\nName both pairs of alternate exterior angles.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n\u22201 and \u22208<br \/>\n\u22202 and \u22207<\/p>\n<p>Explanation:<br \/>\nAlternate exterior angles<br \/>\n\u22201 and \u22208<br \/>\n\u22202 and \u22207<\/p>\n<p>Question 9.<br \/>\nName the relationship between \u2220 3 and \u22206.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nalternate interior angles<\/p>\n<p>Explanation:<br \/>\n\u22203 and \u22206 are alternate interior angles.<br \/>\nAlternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.<\/p>\n<p>Question 10.<br \/>\nName the relationship between \u22204 and \u22206.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nsame-side interior angles<\/p>\n<p>Explanation:<br \/>\n\u22204 and \u22206 are same-side interior angles.<\/p>\n<p><strong>Find each angle measure.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 1: Parallel Lines Cut by a Transversal img 3\" width=\"266\" height=\"215\" \/><\/p>\n<p>Question 11.<br \/>\nm\u2220AGE when m\u2220FHD = 30\u00b0<br \/>\n_________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220AGE = 30\u00b0<\/p>\n<p>Explanation:<br \/>\n\u2220AGE and \u2220FHD are alternate exterior angles.<br \/>\nTherefore, m\u2220AGE = m\u2220FHD = 30\u00b0<br \/>\nm\u2220AGE = 30\u00b0<\/p>\n<p>Question 12.<br \/>\nm\u2220AGH when m\u2220CHF = 150\u00b0<br \/>\n_________ \u00b0<\/p>\n<p>Answer:<br \/>\n150\u00b0<\/p>\n<p>Explanation:<br \/>\n\u2220AGH and \u2220CHF are corresponding angles.<br \/>\nTherefore, m\u2220AGH = m\u2220CHF = 150\u00b0<br \/>\nm\u2220AGH = 150\u00b0<\/p>\n<p>Question 13.<br \/>\nm\u2220CHF when m\u2220BGE = 110\u00b0<br \/>\n_________ \u00b0<\/p>\n<p>Answer:<br \/>\n110\u00b0<\/p>\n<p>Explanation:<br \/>\n\u2220CHF and \u2220BGE are alternate exterior angles.<br \/>\nTherefore, m\u2220CHF = m\u2220BGE = 110\u00b0<br \/>\nm\u2220CHF = 110\u00b0<\/p>\n<p>Question 14.<br \/>\nm\u2220CHG when m\u2220HGA = 120\u00b0<br \/>\n_________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220CHG = 60\u00ba<\/p>\n<p>Explanation:<br \/>\n\u2220CHF and \u2220HGA are same-side interior angles.<br \/>\nm\u2220CHG + m\u2220HGA = 180\u00b0<br \/>\nm\u2220CHG + 120\u00b0 = 180\u00b0<br \/>\nm\u2220CHG = 180 &#8211; 120 = 60<br \/>\nm\u2220CHG = 60\u00ba<\/p>\n<p>Question 15.<br \/>\nm\u2220BGH<br \/>\n_________ \u00b0<\/p>\n<p>Answer:<br \/>\n78\u00ba<\/p>\n<p>Explanation:<br \/>\n\u2220BGH and \u2220GHD are same-side interior angles.<br \/>\nSo, \u2220BGH + \u2220GHD = 180\u00ba<br \/>\n3x + (2x + 50)\u00ba = 180\u00ba<br \/>\n5x = 180\u00ba &#8211; 50\u00ba = 130\u00ba<br \/>\nx = 130\/5 = 26\u00ba<br \/>\n\u2220BGH = 3x\u00ba = 3 \u00d7 26\u00ba = 78\u00ba<br \/>\n\u2220GHD = (2x + 50) += (2 \u00d7 26 + 50) = 102\u00ba<\/p>\n<p>Question 16.<br \/>\nm\u2220GHD<br \/>\n_________ \u00b0<\/p>\n<p>Answer:<br \/>\n102\u00ba<\/p>\n<p>Explanation:<br \/>\n\u2220BGH and \u2220GHD are same-side interior angles.<br \/>\nSo, \u2220BGH + \u2220GHD = 180\u00ba<br \/>\n3x + (2x + 50)\u00ba = 180\u00ba<br \/>\n5x = 180\u00ba &#8211; 50\u00ba = 130\u00ba<br \/>\nx = 130\/5 = 26\u00ba<br \/>\n\u2220BGH = 3x\u00ba = 3 \u00d7 26\u00ba = 78\u00ba<br \/>\n\u2220GHD = (2x + 50) += (2 \u00d7 26 + 50) = 102\u00ba<\/p>\n<p>Question 17.<br \/>\nThe Cross Country Bike Trail follows a straight line where it crosses 350th and 360th Streets. The two streets are parallel to each other. What is the measure of the larger angle formed at the intersection of the bike trail and 360th Street? Explain.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 1: Parallel Lines Cut by a Transversal img 4\" width=\"329\" height=\"189\" \/><br \/>\n_________ \u00b0<\/p>\n<p>Answer:<br \/>\nThe larger angle formed at the intersection of the bike trail and 360th Street is 132\u00ba<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-1-300x151.png\" alt=\"grade 8 chapter 11 image 1\" width=\"300\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-1-300x151.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-1.png 311w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe larger angle formed at the intersection of the bike trail and 360th Street is the angle 5 in our schema. \u22205 and \u22203 are same-side interior angles. Therefore, m\u22205 + m\u22203 = 180\u00ba<br \/>\nm\u22205 + 48\u00ba = 180\u00ba<br \/>\nm\u22205 = 180\u00ba &#8211; 48\u00ba<br \/>\nm\u22205 = 132\u00ba<\/p>\n<p>Question 18.<br \/>\nCritical Thinking How many different angles would be formed by a transversal intersecting three parallel lines? How many different angle measures would there be?<br \/>\n_________ different angles<br \/>\n_________ different angle measures<\/p>\n<p>Answer:<br \/>\n12 different angles<br \/>\n2 different angle measures<\/p>\n<p>Explanation:<br \/>\nThere are 12 different angles formed by a transversal intersecting three parallel lines.<br \/>\nThere are 2 different angle measures:<br \/>\nm\u22201 = m\u22204 = m\u22205 = m\u22208 = m\u22209 = m\u222012<br \/>\nm\u22202 = m\u22203 = m\u22206 = m\u22207 = m\u222010 = m\u222011<\/p>\n<h3><a id=\"Parallel_Lines_Cut_by_a_Transversal_Lesson_Check_\u2013_Page_No._352\"><\/a>Parallel Lines Cut by a Transversal &#8211; Page No. 352<\/h3>\n<p>Question 19.<br \/>\nCommunicate Mathematical Ideas In the diagram at the right, suppose m\u22206 = 125\u00b0. Explain how to find the measures of each of the other seven numbered angles.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 1: Parallel Lines Cut by a Transversal img 5\" width=\"238\" height=\"174\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nm\u22202 = m\u22206 = 125\u00ba because \u22202 and \u22206 are corresponding angles.<br \/>\nm\u22203 = m\u22202 = 125\u00ba because \u22203 and \u22202 are vertical angles.<br \/>\nm\u22207 = m\u22203 = 125\u00ba because \u22207 and \u22203 are corresponding angles.<br \/>\n\u22204 and \u22206 are same-side interior angles.<br \/>\nTherefore, m\u22204 + m\u22206 = 180\u00ba<br \/>\nm\u22204 + 125\u00ba = 180\u00ba<br \/>\nm\u22204 = 180\u00ba &#8211; 125\u00ba<br \/>\nm\u22204 = 55\u00ba<br \/>\nm\u22208 = m\u22204 = 55\u00ba because \u22208 and \u22204 are corresponding angles.<br \/>\nm\u22201 = m\u22204 = 55\u00ba because \u22201 and \u22204 are vertical angles.<br \/>\nm\u22205 = m\u22201 = 55\u00ba because \u22205 and \u22201 are corresponding angles.<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 20.<br \/>\nDraw Conclusions In a diagram showing two parallel lines cut by a transversal, the measures of two same-side interior angles are both given as 3x\u00b0. Without writing and solving an equation, can you determine the measures of both angles? Explain. Then write and solve an equation to find the measures.<\/p>\n<p>Answer:<br \/>\nm\u22201 and m\u22202 are same-side interior angles is 180\u00ba<br \/>\nTherefore, m\u22201 + m\u22202 = 180\u00ba<br \/>\n3x + 3x = 180\u00ba<br \/>\n6x = 180\u00ba<br \/>\nx = 180\/6 = 30<br \/>\nm\u22201 = m\u22202 = 3x = 3(30) = 90\u00ba<\/p>\n<p>Question 21.<br \/>\nMake a Conjecture Draw two parallel lines and a transversal. Choose one of the eight angles that are formed. How many of the other seven angles are congruent to the angle you selected? How many of the other seven angles are supplementary to your angle? Will your answer change if you select a different angle?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-7902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-3-204x300.jpg\" alt=\"grade 8 chapter 11 image 3\" width=\"154\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-3-204x300.jpg 204w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-3.jpg 246w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\nWe have to select \u2220a form of eight angles that are formed. There are two other angles that are congruent to the angle \u2220a. Two other angles are \u2220e and \u2220g.<br \/>\nThere are no supplementary to \u2220a.<br \/>\nIf we select a different angle then the answer will also change.<\/p>\n<p>Question 22.<br \/>\nCritique Reasoning In the diagram at the right, \u22202, \u22203, \u22205, and\u22208 are all congruent, and\u22201, \u22204, \u22206, and \u22207 are all congruent. Aiden says that this is enough information to conclude that the diagram shows two parallel lines cut by a transversal. Is he correct? Justify your answer.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 1: Parallel Lines Cut by a Transversal img 6\" width=\"205\" height=\"192\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThis is not enough information to conclude that the diagram shows two parallel lines cut by a transversal. Because \u22202 and \u22203 are same-side interior angles. But \u22205 and \u22208 are not congruent with each other. And \u22206 and \u22207 are same-side interior angles. But \u22201 and \u22204 are not congruent with each other.<\/p>\n<h3><a id=\"Angle_Theorems_for_Triangles_\u2013_Page_No._358\"><\/a>Guided Practice &#8211; Angle Theorems for Triangles &#8211; Page No. 358<\/h3>\n<p><strong>Find each missing angle measure.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-7.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 7\" width=\"183\" height=\"117\" \/><br \/>\nm\u2220M = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220M = 71\u00ba<\/p>\n<p>Explanation:<br \/>\nFrom the Triangle Sum Theorem,<br \/>\nm\u2220L + m\u2220N + m\u2220M = 180\u00ba<br \/>\n78\u00ba + 31\u00ba + m\u2220M = 180\u00ba<br \/>\n109\u00ba + m\u2220M = 180\u00ba<br \/>\nm\u2220M = 180\u00ba &#8211; 109\u00ba<br \/>\nm\u2220M = 71\u00ba<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-8.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 8\" width=\"327\" height=\"118\" \/><br \/>\nm\u2220Q = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220Q = 30\u00ba<\/p>\n<p>Explanation:<br \/>\nFrom the Triangle Sum Theorem,<br \/>\nm\u2220Q + m\u2220S + m\u2220R = 180\u00ba<br \/>\nm\u2220Q + 24\u00ba + 126\u00ba = 180\u00ba<br \/>\nm\u2220Q + 150\u00ba = 180\u00ba<br \/>\nm\u2220Q = 180\u00ba &#8211; 150\u00ba<br \/>\nm\u2220Q = 30\u00ba<\/p>\n<p><strong>Use the Triangle Sum Theorem to find the measure of each angle in degrees.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-9.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 9\" width=\"192\" height=\"118\" \/><br \/>\nm\u2220T = _________ \u00b0<br \/>\nm\u2220V = _________ \u00b0<br \/>\nm\u2220U = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220T = 88\u00b0<br \/>\nm\u2220V = 63\u00b0<br \/>\nm\u2220U = 29\u00b0<\/p>\n<p>Explanation:<br \/>\nFrom the Triangle Sum Theorem,<br \/>\nm\u2220U + m\u2220T + m\u2220V = 180\u00ba<br \/>\n(2x + 5)\u00ba + (7x + 4)\u00ba + (5x + 3)\u00ba = 180\u00ba<br \/>\n2x\u00ba + 5\u00ba + 7x\u00ba + 4\u00ba + 5x\u00ba + 3\u00ba = 180\u00ba<br \/>\n14x\u00ba + 12\u00ba = 180\u00ba<br \/>\n14x\u00ba = 168\u00ba<br \/>\nx = 168\/14 = 12<br \/>\nSubstitute x value to find the angles<br \/>\nm\u2220U = (2x + 5)\u00ba = ((2 . 12) + 5)\u00ba = 29\u00ba<br \/>\nm\u2220U = 29\u00ba<br \/>\nm\u2220T = (7x + 4)\u00ba = ((7 . 12) + 4)\u00ba = 88\u00ba<br \/>\nm\u2220T = 88\u00ba<br \/>\nm\u2220V = (5x + 3)\u00ba = ((5 . 12) + 3)\u00ba = 63\u00ba<br \/>\nm\u2220V = 63\u00ba<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-10.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 10\" width=\"179\" height=\"146\" \/><br \/>\nm\u2220X = _________ \u00b0<br \/>\nm\u2220Y = _________ \u00b0<br \/>\nm\u2220Z = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220X = 90\u00b0<br \/>\nm\u2220Y = 45 \u00b0<br \/>\nm\u2220Z = 45\u00b0<\/p>\n<p>Explanation:<br \/>\nFrom the Triangle Sum Theorem,<br \/>\nm\u2220X + m\u2220Y + m\u2220Z = 180\u00ba<br \/>\nn\u00ba + (1\/2 . n)\u00ba + (1\/2 . n)\u00ba = 180\u00ba<br \/>\n2n\u00ba = 180\u00ba<br \/>\nn = 90<br \/>\nSubstitute n values to find the angles<br \/>\nm\u2220X = n\u00ba = 90\u00ba<br \/>\nm\u2220X = 90\u00ba<br \/>\nm\u2220Y = (1\/2 . n)\u00ba = (1\/2 . 90)\u00ba = 45\u00ba<br \/>\nm\u2220Y = 45\u00ba<br \/>\nm\u2220Z = (1\/2 . n)\u00ba = (1\/2 . 90)\u00ba = 45\u00ba<br \/>\nm\u2220Z = 45\u00ba<\/p>\n<p><strong>Use the Exterior Angle Theorem to find the measure of each angle in degrees.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-11.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 11\" width=\"290\" height=\"144\" \/><br \/>\nm\u2220C = _________ \u00b0<br \/>\nm\u2220D = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220C = 40\u00b0<br \/>\nm\u2220D = 76\u00b0<\/p>\n<p>Explanation:<br \/>\nGiven m\u2220C = 4y\u00b0, m\u2220D = (7y + 6)\u00b0, m\u2220E = 116\u00b0<br \/>\nBy using exterior angle theorem,<br \/>\n\u2220DEC + \u2220DEF = 180\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-4-300x158.jpg\" alt=\"grade 8 chapter 11 image 4\" width=\"300\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-4-300x158.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-4.jpg 574w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\u2220DEC + 116\u00b0 = 180\u00b0<br \/>\n\u2220E = \u2220DEC = 180\u00b0 &#8211; 116\u00b0 = 64\u00b0<br \/>\nThe sum of the angles of a traingle = 180\u00b0<br \/>\n\u2220C +\u2220D + \u2220E = 180\u00b0<br \/>\n4y\u00b0 + (7y + 6)\u00b0+ 64\u00b0 = 180\u00b0<br \/>\n11y\u00b0 + 70\u00b0 = 180\u00b0<br \/>\n11y\u00b0 = 180\u00b0 &#8211; 70\u00b0 = 110\u00b0<br \/>\ny = 10<br \/>\n\u2220C = 4y\u00b0 = 4. 10 = 40\u00b0<br \/>\n\u2220D = (7y + 6)\u00b0 = ((7 . 10)\u00a0 + 6)\u00b0 = (70 + 6)\u00b0 = 76\u00b0<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-12.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 12\" width=\"329\" height=\"148\" \/><br \/>\nm\u2220L = _________ \u00b0<br \/>\nm\u2220M = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220L = 129\u00b0<br \/>\nm\u2220M = 32\u00b0<\/p>\n<p>Explanation:<br \/>\nGiven that m\u2220M = (5z &#8211; 3)\u00b0, m\u2220L = (18z + 3)\u00b0, m\u2220JKM\u00a0= 161\u00b0<br \/>\nFrom the Exterior Angle Theorem,<br \/>\nm\u2220M + m\u2220L = m\u2220JKM<br \/>\n(5z &#8211; 3)\u00b0 + (18z + 3)\u00b0 = 161\u00b0<br \/>\n5z\u00b0 &#8211; 3\u00b0 + 18z\u00b0 + 3\u00b0 = 161\u00b0<br \/>\n23z\u00b0 = 161\u00b0<br \/>\nz = 161\/23 = 7<br \/>\nSubstitute z values to find the angles<br \/>\nm\u2220M = (5z &#8211; 3)\u00b0 = ((5 . 7) &#8211; 3)\u00b0 = 32\u00b0<br \/>\nm\u2220L = (18z + 3)\u00b0 = ((18 . 7) + 3)\u00b0 = 129\u00b0<br \/>\nFrom the Triangle Sum Theorem,<br \/>\nm\u2220M + m\u2220L + m\u2220LKM = 180\u00ba<br \/>\n32\u00ba + 129\u00ba + m\u2220LKM = 180\u00ba<br \/>\n161\u00ba + m\u2220LKM = 180\u00ba<br \/>\nm\u2220LKM = 19\u00ba<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 7.<br \/>\nDescribe the relationships among the measures of the angles of a triangle.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe sum of all measures of the interior angles of a triangle is 180\u00b0. The measure of an exterior angle of a triangle is equal to the sum of its remote interior angles.<\/p>\n<h3><a id=\"Angle_Theorems_for_Triangles_\u2013_Page_No._359\"><\/a>11.2 Independent Practice &#8211; Angle Theorems for Triangles &#8211; Page No. 359<\/h3>\n<p><strong>Find the measure of each angle.<\/strong><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-13.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 13\" width=\"297\" height=\"172\" \/><br \/>\nm\u2220E = _________ \u00b0<br \/>\nm\u2220F = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220E = 41\u00b0<br \/>\nm\u2220F = 41\u00b0<\/p>\n<p>Explanation:<br \/>\nm\u2220E = x\u00b0, m\u2220F = x\u00b0,\u00a0 m\u2220D = 98\u00b0<br \/>\nFrom the Triangle Sum Theorem, sum of the angles of the traingle is 180\u00b0<br \/>\nm\u2220E + m\u2220D + m\u2220F = 180\u00b0<br \/>\nx + 98 + x = 180\u00b0<br \/>\n2x + 98 = 180\u00b0<br \/>\n2x = 82\u00b0<br \/>\nx = 41\u00b0<br \/>\nSo, m\u2220E = 41\u00b0<br \/>\nm\u2220F = 41\u00b0<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-14.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 14\" width=\"286\" height=\"185\" \/><br \/>\nm\u2220T = _________ \u00b0<br \/>\nm\u2220V = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220T = 60\u00b0<br \/>\nm\u2220V = 30\u00b0<\/p>\n<p>Explanation:<br \/>\nm\u2220W = 90\u00b0, m\u2220T = 2x\u00b0,\u00a0 m\u2220V = x\u00b0<br \/>\nFrom the Triangle Sum Theorem, sum of the angles of the traingle is 180\u00b0<br \/>\nm\u2220T + m\u2220V + m\u2220W = 180\u00b0<br \/>\n2x + x + 90 = 180\u00b0<br \/>\n3x = 90\u00b0<br \/>\nx = 30\u00b0<br \/>\nSo, m\u2220T = 2x\u00b0 = 2 . 30\u00b0 = 60\u00b0<br \/>\nm\u2220V = x\u00b0 = 30\u00b0<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-15.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 15\" width=\"276\" height=\"191\" \/><br \/>\nm\u2220G = _________ \u00b0<br \/>\nm\u2220H = _________ \u00b0<br \/>\nm\u2220J = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220G = 75\u00b0<br \/>\nm\u2220H = 60\u00b0<br \/>\nm\u2220J = 45\u00b0<\/p>\n<p>Explanation:<br \/>\nm\u2220G = 5x\u00b0, m\u2220H = 4x\u00b0,\u00a0 m\u2220J = 3x\u00b0<br \/>\nFrom the Triangle Sum Theorem, sum of the angles of the traingle is 180\u00b0<br \/>\nm\u2220G + m\u2220H + m\u2220J = 180\u00b0<br \/>\n5x + 4x + 3x = 180\u00b0<br \/>\n12x = 90\u00b0<br \/>\nx = 15\u00b0<br \/>\nSo, m\u2220G = 5x\u00b0 = 5 . 15\u00b0 = 75\u00b0<br \/>\nm\u2220H = 4x\u00b0 = 4. 15\u00b0 = 60\u00b0<br \/>\nm\u2220J = 3x\u00b0 = 3. 15\u00b0 = 45\u00b0<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-16.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 16\" width=\"303\" height=\"139\" \/><br \/>\nm\u2220Q = _________ \u00b0<br \/>\nm\u2220P = _________ \u00b0<br \/>\nm\u2220QRP = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220Q = 98\u00b0<br \/>\nm\u2220P = 55\u00b0<br \/>\nm\u2220QRP = 27\u00b0<\/p>\n<p>Explanation:<br \/>\nGiven that m\u2220Q = (3y + 5)\u00b0, m\u2220P = (2y &#8211; 7)\u00b0, m\u2220QRS = 153\u00b0<br \/>\nFrom the exterior angle Theorem,<br \/>\n\u2220QRS + \u2220QRP = 180\u00b0<br \/>\n153\u00b0 + \u2220QRP = 180\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-5-300x153.jpg\" alt=\"grade 8 chapter 11 image 5\" width=\"300\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-5-300x153.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-5.jpg 540w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nm\u2220R = m\u2220QRP = 180\u00b0 &#8211; 153\u00b0 = 27\u00b0<br \/>\nFrom the Triangle Sum Theorem, the sum of the angles of the triangle is 180\u00b0<br \/>\nm\u2220P + m\u2220Q + m\u2220R = 180\u00b0<br \/>\n(3y + 5)\u00b0 + (2y &#8211; 7)\u00b0+ 27\u00b0 = 180\u00b0<br \/>\n5y\u00b0 + 25 = 180\u00b0<br \/>\n5y\u00b0 = 155\u00b0<br \/>\ny = 31\u00b0<br \/>\nm\u2220Q = (3y + 5)\u00b0 = ((3 . 31\u00b0) + 5)\u00b0 = 98\u00b0<br \/>\nm\u2220P = (2y &#8211; 7)\u00b0 = ((2. 31\u00b0 &#8211; 7)\u00b0 = 55\u00b0<br \/>\nm\u2220QRP = 27\u00b0<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-17.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 17\" width=\"303\" height=\"153\" \/><br \/>\nm\u2220ACB = _________ \u00b0<br \/>\nm\u2220DCE = _________ \u00b0<br \/>\nm\u2220BCD = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220ACB = 44\u00b0<br \/>\nm\u2220DCE = 35\u00b0<br \/>\nm\u2220BCD = 101\u00b0<\/p>\n<p>Explanation:<br \/>\nIn traingle ABC, m\u2220A = 78\u00b0, m\u2220B = 58\u00b0, m\u2220ACB = ?\u00b0<br \/>\nFrom the Triangle Sum Theorem, the sum of the angles of the triangle is 180\u00b0<br \/>\nm\u2220A + m\u2220B + m\u2220ACB = 180\u00b0<br \/>\n78\u00b0 + 58\u00b0 + m\u2220ACB = 180\u00b0<br \/>\nm\u2220ACB = 180\u00b0 &#8211; 136\u00b0<br \/>\nm\u2220ACB = 44\u00b0<br \/>\nIn traingle CDE, m\u2220D = 85\u00b0, m\u2220E = 60\u00b0, m\u2220CDE = ?\u00b0<br \/>\nFrom the Triangle Sum Theorem, the sum of the angles of the triangle is 180\u00b0<br \/>\nm\u2220D + m\u2220E + m\u2220CDE = 180\u00b0<br \/>\n85\u00b0 + 60\u00b0 + m\u2220CDE = 180\u00b0<br \/>\nm\u2220CDE = 180\u00b0 &#8211; 145\u00b0<br \/>\nm\u2220CDE = 35\u00b0<br \/>\nFrom the Exterior Angle Theorem,<br \/>\nm\u2220ACB + m\u2220CDE + m\u2220BCD = 180\u00b0<br \/>\n44\u00b0 + 35\u00b0 + m\u2220BCD = 180\u00b0<br \/>\nm\u2220BCD = 180\u00b0 &#8211; 79\u00b0<br \/>\nm\u2220BCD = 101\u00b0<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-18.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 18\" width=\"313\" height=\"146\" \/><br \/>\nm\u2220K = _________ \u00b0<br \/>\nm\u2220L = _________ \u00b0<br \/>\nm\u2220KML = _________ \u00b0<br \/>\nm\u2220LMN = _________ \u00b0<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\nm\u2220K = 2x\u00b0, m\u2220L = 3x\u00b0, m\u2220KML = x\u00b0<br \/>\nSo, From the Triangle Sum Theorem, the sum of the angles of the triangle is 180\u00b0.<br \/>\nm\u2220K + m\u2220L + m\u2220KML = 180\u00b0<br \/>\n2x\u00b0 + 3x\u00b0 + x\u00b0 = 180\u00b0<br \/>\n6x\u00b0 = 180\u00b0<br \/>\nx= 30\u00b0<br \/>\n\u2220KML = x = 30\u00b0<br \/>\n\u2220L = 3x = 3 . 30\u00b0 = 90\u00b0<br \/>\n\u2220K = 2x = 2 . 30\u00b0 = 60\u00b0<br \/>\nFrom the Exterior Angle Theorem,<br \/>\n\u2220KML + \u2220LMN = 180\u00b0<br \/>\n\u2220LMN = 180\u00b0 &#8211; 30\u00b0 = 150\u00b0<\/p>\n<p>Question 14.<br \/>\nMultistep The second angle in a triangle is five times as large as the first. The third angle is two-thirds as large as the first. Find the angle measures.<br \/>\nThe measure of the first angle: _________ \u00b0<br \/>\nThe measure of the second angle: _________ \u00b0<br \/>\nThe measure of the third angle: _________ \u00b0<\/p>\n<p>Answer:<br \/>\nThe measure of the first angle: 27\u00b0<br \/>\nThe measure of the second angle: 135\u00b0<br \/>\nThe measure of the third angle: 18\u00b0<\/p>\n<p>Explanation:<br \/>\nLet us name the angles of a triangle as \u22201, \u22202, \u22203.<br \/>\nConsider \u22201 as x.<br \/>\n\u22202 is 5 times as large as the first.<br \/>\n\u22202 = 5x<br \/>\nAlso, \u22203 = 2\/3 . x<br \/>\nSo, From the Triangle Sum Theorem, the sum of the angles of the triangle is 180\u00b0.<br \/>\nx+ 5x + (2\/3 . x) = 180\u00b0<br \/>\n20x = 540\u00b0<br \/>\nx = 27\u00b0<br \/>\nSo, \u22201 = x = 27\u00b0<br \/>\n\u22202 = 5x = 5 . 27\u00b0 = 135\u00b0<br \/>\n\u22203 = 2\/3 . x = 2\/3 . 27\u00b0 = 18\u00b0<br \/>\nThe measure of the first angle: 27\u00b0<br \/>\nThe measure of the second angle: 135\u00b0<br \/>\nThe measure of the third angle: 18\u00b0<\/p>\n<h3><a id=\"Angle_Theorems_for_Triangles_Lesson_Check_\u2013_Page_No._360\"><\/a>Angle Theorems for Triangles &#8211; Page No. 360<\/h3>\n<p>Question 15.<br \/>\nAnalyze Relationships Can a triangle have two obtuse angles? Explain.<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nNo; a triangle can NOT have two obtuse angles<\/p>\n<p>Explanation:<br \/>\nThe measure of an obtuse angle is greater than 90\u00b0. Two obtuse angles and the third angle would have a sum greater than 180\u00b0<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 16.<br \/>\nCritical Thinking Explain how you can use the Triangle Sum Theorem to find the measures of the angles of an equilateral triangle.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nAll angles have the same measure in an equilateral triangle<\/p>\n<p>Explanation:<br \/>\nUsing the Triangle Sum Theorem,<br \/>\n\u2220x + \u2220x + \u2220x = 180\u00b0<br \/>\n3\u2220x = 180\u00b0<br \/>\n\u2220x = 60\u00b0<br \/>\nAll angles have the same measure in an equilateral triangle<\/p>\n<p>Question 17.<br \/>\na. Draw Conclusions Find the sum of the measures of the angles in quadrilateral ABCD. (Hint: Draw diagonal \\(\\overline { AC } \\). How can you use the figures you have formed to find the sum?)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-19.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 2: Angle Theorems for Triangles img 19\" width=\"177\" height=\"103\" \/><br \/>\nSum: _________ \u00b0<\/p>\n<p>Answer:<br \/>\nSum: 360\u00b0<\/p>\n<p>Question 17.<br \/>\nb. Make a Conjecture Write a \u201cQuadrilateral Sum Theorem.\u201d Explain why you think it is true.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nThe sum of the angle measures of a quadrilateral is 360\u00b0<br \/>\nAny quadrilateral can be divided into two triangles (180 + 180 = 360)<\/p>\n<p>Question 18.<br \/>\nCommunicate Mathematical Ideas Describe two ways that an exterior angle of a triangle is related to one or more of the interior angles.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nAn exterior angle and it&#8217;s an adjacent interior angle equal 180\u00b0<br \/>\nAn exterior angle equals the sum of the two remote interior angles.<\/p>\n<h3><a id=\"Angle-Angle_Similarity_\u2013_Page_No._366\"><\/a>Guided Practice &#8211; Angle-Angle Similarity &#8211; Page No. 366<\/h3>\n<p>Question 1.<br \/>\nExplain whether the triangles are similar. Label the angle measures in the figure.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-20.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 3: Angle-Angle Similarity img 20\" width=\"478\" height=\"117\" \/><br \/>\nType below:<br \/>\n___________<br \/>\n\u25b3ABC has angle measures _______and \u25b3DEF has angle measures______. Because _______in one triangle are congruent to ______in the other triangle, the triangles are_____.<\/p>\n<p>Answer:<br \/>\n\u25b3ABC has angle measures 40\u00b0, 30\u00b0, and 109\u00b0 and \u25b3DEF has angle measures 41\u00b0, 109\u00b0, and 30\u00b0. Because 2\u2220s in one triangle are congruent to in the other triangle, the triangles similar.<\/p>\n<p>Question 2.<br \/>\nA flagpole casts a shadow 23.5 feet long. At the same time of day, Mrs. Gilbert, who is 5.5 feet tall, casts a shadow that is 7.5 feet long. How tall in feet is the flagpole? Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-21.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 3: Angle-Angle Similarity img 21\" width=\"570\" height=\"186\" \/><br \/>\n_________ ft<\/p>\n<p>Answer:<br \/>\n17.2 ft<\/p>\n<p>Explanation:<br \/>\nIn similar triangles, corresponding side lengths are proportional.<br \/>\n5.5\/7.5 = h\/23.5<br \/>\nh (7.5) = 129.25<br \/>\nh = 129.25\/7.5<br \/>\nh = 17.23<br \/>\nRounding to the nearest tenth<br \/>\nh = 17.2 feet<\/p>\n<p>Question 3.<br \/>\nTwo transversals intersect two parallel lines as shown. Explain whether \u25b3ABC and \u25b3DEC are similar.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-22.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 3: Angle-Angle Similarity img 22\" width=\"309\" height=\"148\" \/><br \/>\n\u2220BAC and\u2220EDC are ___________ since they are ___________.<br \/>\n\u2220ABC and\u2220DEC are ___________ since they are ___________.<br \/>\nBy ________, \u25b3ABC and\u25b3DEC are ___________.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n\u2220BAC and\u2220EDC are congruent since they are alt. interior \u2220s<br \/>\n\u2220ABC and\u2220DEC are congruent since they are alt. interior \u2220s.<br \/>\nBy AA similarity, \u25b3ABC and\u25b3DEC are similar.<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you determine when two triangles are similar?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nIf 2 angles of one triangle are congruent to 2 angles of another triangle, the triangles are similar by the Angle-Angle Similarity Postulate<\/p>\n<h3><a id=\"Angle-Angle_Similarity_\u2013_Page_No._367\"><\/a>11.3 Independent Practice &#8211; Angle-Angle Similarity &#8211; Page No. 367<\/h3>\n<p><strong>Use the diagrams for Exercises 5\u20137.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-23.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 3: Angle-Angle Similarity img 23\" width=\"610\" height=\"194\" \/><\/p>\n<p>Question 5.<br \/>\nFind the missing angle measures in the triangles.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nm\u2220B = 42\u00b0<br \/>\nm\u2220F = 69\u00b0<br \/>\nm\u2220H = 64\u00b0<br \/>\nm\u2220K = 53\u00b0<\/p>\n<p>Explanation:<br \/>\nUsing the Triangle Sum Theorem,<br \/>\nm\u2220A + m\u2220B + m\u2220C = 180\u00b0<br \/>\n85\u00b0 + m\u2220B + 53\u00b0 = 180\u00b0<br \/>\n138\u00b0 + m\u2220B = 180\u00b0<br \/>\nm\u2220B = 180\u00b0 &#8211; 138\u00b0<br \/>\nm\u2220B = 42\u00b0<br \/>\nUsing the Triangle Sum Theorem,<br \/>\nm\u2220D + m\u2220E + m\u2220F = 180\u00b0<br \/>\nWe substitute the given angle measures and we solve for m\u2220F<br \/>\n64\u00b0 + 47\u00b0 + m\u2220F = 180\u00b0<br \/>\n111\u00b0 + m\u2220F = 180\u00b0<br \/>\nm\u2220F = 180\u00b0 &#8211; 111\u00b0<br \/>\nm\u2220F = 69\u00b0<br \/>\nUsing the Triangle Sum Theorem,<br \/>\nm\u2220G + m\u2220H + m\u2220J = 180\u00b0<br \/>\nWe substitute the given angle measures and we solve for m\u2220H<br \/>\n47\u00b0 + m\u2220H + 69\u00b0 = 180\u00b0<br \/>\n116\u00b0 + m\u2220H = 180\u00b0<br \/>\nm\u2220H = 180\u00b0 &#8211; 116\u00b0<br \/>\nm\u2220H = 64\u00b0<br \/>\nUsing the Triangle Sum Theorem,<br \/>\nm\u2220J + m\u2220K + m\u2220L = 180\u00b0<br \/>\nWe substitute the given angle measures and we solve for m\u2220K<br \/>\n85\u00b0 + m\u2220K + 42\u00b0 = 180\u00b0<br \/>\n127\u00b0 + m\u2220K = 180\u00b0<br \/>\nm\u2220K = 180\u00b0 &#8211; 127\u00b0<br \/>\nm\u2220K = 53\u00b0<\/p>\n<p>Question 6.<br \/>\nWhich triangles are similar?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n\u25b3ABC and \u25b3JKL are similar because their corresponding angles are congruent. Also, \u25b3DEF and \u25b3GHJ are similar because their corresponding is congruent.<\/p>\n<p>Question 7.<br \/>\nAnalyze Relationships Determine which angles are congruent to the angles in \u25b3ABC.<br \/>\n\u2220A \u2245 \u2220 ________<br \/>\n\u2220B \u2245 \u2220 ________<br \/>\n\u2220C \u2245 \u2220 ________<\/p>\n<p>Answer:<br \/>\n\u25b3JKL \u2245 \u25b3ABC<\/p>\n<p>Explanation:<br \/>\n\u25b3JKL has angle measures that are the same as those is \u25b3ABC<br \/>\n\u2220A \u2245 \u2220 J<br \/>\n\u2220B \u2245 \u2220 L<br \/>\n\u2220C \u2245 \u2220 K<br \/>\nTherefore, they are congruent.<\/p>\n<p>Question 8.<br \/>\nMultistep A tree casts a shadow that is 20 feet long. Frank is 6 feet tall,and while standing next to the tree he casts a shadow that is 4 feet long.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-24.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 3: Angle-Angle Similarity img 24\" width=\"180\" height=\"204\" \/><br \/>\na. How tall is the tree?<br \/>\nh = ________ ft<\/p>\n<p>Answer:<br \/>\nh = 30 ft<\/p>\n<p>Explanation:<br \/>\nIn similar triangles, corresponding side lengths are proportional.<br \/>\n20\/4 = h\/6<br \/>\n5 = h\/6<br \/>\nh = 30<br \/>\nThe tree is 30 feet tall.<\/p>\n<p>Question 8.<br \/>\nb. How much taller is the tree than Frank?<br \/>\n________ ft<\/p>\n<p>Answer:<br \/>\n24 ft<\/p>\n<p>Explanation:<br \/>\n30 &#8211; 6 = 24<br \/>\nThe tree is 24 feet taller than Frank.<\/p>\n<p>Question 9.<br \/>\nRepresent Real-World Problems Sheila is climbing on a ladder that is attached against the side of a jungle gym wall. She is 5 feet off the ground and 3 feet from the base of the ladder, which is 15 feet from the wall. Draw a diagram to help you solve the problem. How high up the wall is the top of the ladder?<br \/>\n________ ft<\/p>\n<p>Answer:<br \/>\n25 ft<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/09\/grade-8-chapter-11-image-6.gif\" alt=\"grade 8 chapter 11 image 6\" width=\"279\" height=\"249\" \/><br \/>\n3\/15 = 5\/h<br \/>\n15 \u00d73 = 3h<br \/>\n75 = 3h<br \/>\nh = 75\/3 = 25<\/p>\n<p>Question 10.<br \/>\nJustify Reasoning Are two equilateral triangles always similar? Explain.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nyes; two equilateral triangles are always similar.<br \/>\nEach angle of an equilateral triangle is 60\u00b0. Since both triangles are equilateral then they are similar.<\/p>\n<h3><a id=\"Angle-Angle_Similarity_Lesson_Check_\u2013_Page_No._368\"><\/a>Angle-Angle Similarity &#8211; Page No. 368<\/h3>\n<p>Question 11.<br \/>\nCritique Reasoning Ryan calculated the missing measure in the diagram shown. What was his mistake?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-25.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Lesson 3: Angle-Angle Similarity img 25\" width=\"288\" height=\"179\" \/><br \/>\n\\(\\frac{3.4}{6.5}=\\frac{h}{19.5}\\)<br \/>\n19.5 \u00d7 \\(\\frac{3.4}{6.5}=\\frac{h}{19.5}\\) \u00d7 19.5<br \/>\n\\(\\frac{66.3}{6.5}\\) = h<br \/>\n10.2cm = h<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nIn the first line, Ryan did not take the sum of 6.5 and 19.5 to get the denominator on the right.<br \/>\nThe denominator on the right should be 26 instead of 19.5<br \/>\nthe correct value for h<br \/>\n3.4\/6.5 = h\/26<br \/>\nh = (3.4\/6.5) \u00d7 26<br \/>\nh = 13.6cm<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 12.<br \/>\nCommunicate Mathematical Ideas For a pair of triangular earrings, how can you tell if they are similar? How can you tell if they are congruent?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nThe earrings are similar if two angle measures of one are equal to two angle measures of the other.<br \/>\nThe earrings are congruent if they are similar and if the side lengths of one are equal to the side lengths of the other.<\/p>\n<p>Question 13.<br \/>\nCritical Thinking When does it make sense to use similar triangles to measure the height and length of objects in real life?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nIf the item is too tall or the distance is too long to measure directly, similar triangles can help with measuring.<\/p>\n<p>Question 14.<br \/>\nJustify Reasoning Two right triangles on a coordinate plane are similar but not congruent. Each of the legs of both triangles are extended by 1 unit, creating two new right triangles. Are the resulting triangles similar? Explain using an example.<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nTwo triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional. If each of the legs of both triangles is extended by 1 unit, the ratio between proportional sides does not change. Therefore, the resulting triangles are similar.<\/p>\n<h3><a id=\"Model_Quiz_\u2013_Page_No._369\"><\/a>Ready to Go On? &#8211; Model Quiz &#8211; Page No. 369<\/h3>\n<p><strong>11.1 Parallel Lines Cut by a Transversal<\/strong><\/p>\n<p><strong>In the figure, line p || line q. Find the measure of each angle if m\u22208 = 115\u00b0.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-26.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Model Quiz img 26\" width=\"230\" height=\"157\" \/><\/p>\n<p>Question 1.<br \/>\nm\u22207 = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u22207 = 65\u00b0<\/p>\n<p>Explanation:<br \/>\nAccording to the exterior angle theorem,<br \/>\nm\u22207 + m\u22208 = 180\u00b0<br \/>\nm\u22207 + 115\u00b0\u00a0= 180\u00b0<br \/>\nm\u22207 = 180\u00b0 &#8211; 115\u00b0<br \/>\nm\u22207 = 65\u00b0<\/p>\n<p>Question 2.<br \/>\nm\u22206 = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u22206 = 115\u00b0<\/p>\n<p>Explanation:<br \/>\nFrom the given figure, Line P is parallel to line Q. So, the angles given in line P is equal to the angles in line Q. They are corresponding angles.<br \/>\nSo, m\u22208 is parallel is m\u22206 or m\u22208 = m\u22206 = 115\u00b0<\/p>\n<p>Question 3.<br \/>\nm\u22201 = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u22201 = 115\u00b0<\/p>\n<p>Explanation:<br \/>\n\u22201 and \u22206 are alternative exterior angles.<br \/>\nSo, m\u22201 = m\u22206 = 115\u00b0<\/p>\n<p><strong>11.2 Angle Theorems for Triangles<\/strong><\/p>\n<p><strong>Find the measure of each angle.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-27.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Model Quiz img 27\" width=\"238\" height=\"163\" \/><\/p>\n<p>Question 4.<br \/>\nm\u2220A = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220A = 48\u00b0<\/p>\n<p>Explanation:<br \/>\nm\u2220A + m\u2220B + m\u2220C = 180\u00b0<br \/>\n4y\u00b0 + (3y + 22)\u00b0 + 74\u00b0 = 180\u00b0<br \/>\n7y = 180 &#8211; 96 = 84<br \/>\ny = 12\u00b0<br \/>\nm\u2220A = 4y\u00b0 = 4 (12\u00b0) = 48\u00b0<br \/>\nm\u2220B = (3y + 22)\u00b0 = (3(12\u00b0) + 22)\u00b0 = 58\u00b0<\/p>\n<p>Question 5.<br \/>\nm\u2220B = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220B = 58\u00b0<\/p>\n<p>Explanation:<br \/>\nm\u2220A + m\u2220B + m\u2220C = 180\u00b0<br \/>\n4y\u00b0 + (3y + 22)\u00b0 + 74\u00b0 = 180\u00b0<br \/>\n7y = 180 &#8211; 96 = 84<br \/>\ny = 12\u00b0<br \/>\nm\u2220A = 4y\u00b0 = 4 (12\u00b0) = 48\u00b0<br \/>\nm\u2220B = (3y + 22)\u00b0 = (3(12\u00b0) + 22)\u00b0 = 58\u00b0<\/p>\n<p>Question 6.<br \/>\nm\u2220BCA = _________ \u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220BCA = 74\u00b0<\/p>\n<p>Explanation:<br \/>\nm\u2220BCD + m\u2220BCA = 180\u00b0<br \/>\n106\u00b0 + m\u2220BCA = 180\u00b0<br \/>\nm\u2220BCA = 180\u00b0 &#8211; 106\u00b0<br \/>\nm\u2220BCA = 74\u00b0<br \/>\nSo, m\u2220BCA = 74\u00b0<\/p>\n<p><strong>11.3 Angle-Angle Similarity<\/strong><\/p>\n<p><strong>Triangle FEG is similar to triangle IHJ. Find the missing values.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-28.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Model Quiz img 28\" width=\"407\" height=\"150\" \/><\/p>\n<p>Question 7.<br \/>\nx = _________<\/p>\n<p>Answer:<br \/>\nx = 16<\/p>\n<p>Explanation:<br \/>\nIn similar triangles, corresponding side lengths are proportional.<br \/>\nHJ\/EG = IJ\/FG<br \/>\n(x + 12)\/42 = 40\/60<br \/>\n(x + 12)\/42 = 4\/6<br \/>\n6x = 96<br \/>\nx = 16<\/p>\n<p>Question 8.<br \/>\ny = _________<\/p>\n<p>Answer:<br \/>\ny = 9<\/p>\n<p>Explanation:<br \/>\nIn similar triangles, corresponding side lengths are congruent.<br \/>\nm\u2220HJI = m\u2220EGF<br \/>\n(5y + 7)\u00b0 = 52\u00b0<br \/>\n5y\u00b0 + 7\u00b0 = 52\u00b0<br \/>\n5y\u00b0 = 45\u00b0<br \/>\ny = 9<\/p>\n<p>Question 9.<br \/>\nm\u2220H = _________\u00b0<\/p>\n<p>Answer:<br \/>\nm\u2220H = 92\u00b0<\/p>\n<p>Explanation:<br \/>\nUsing the Triangle Sum Theorem,<br \/>\nm\u2220E + m\u2220F + m\u2220G = 180\u00b0<br \/>\nWe substitute the given angle measures and we solve for m\u2220E<br \/>\nm\u2220E + 36\u00b0 + 52\u00b0 = 180\u00b0<br \/>\nm\u2220E + 88\u00b0 = 180\u00b0<br \/>\nm\u2220E = 92\u00b0<br \/>\nIn similar angles, corresponding side lengths are congruent<br \/>\nm\u2220H = m\u2220E<br \/>\nm\u2220H = 92\u00b0<\/p>\n<p><strong>ESSENTIAL QUESTION<\/strong><\/p>\n<p>Question 10.<br \/>\nHow can you use similar triangles to solve real-world problems?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nwe know that if two triangles are similar, then their corresponding angles are congruent and the lengths of their corresponding sides are proportional. We can use this to determine values that we cannot measure directly. For example, we can calculate the length of the tree if we measure its shadow and our shadow on a sunny day.<\/p>\n<h3><a id=\"Mixed_Review_\u2013_Page_No._370\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 370<\/h3>\n<p><strong>Use the figure for Exercises 1 and 2.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-29.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Mixed Review img 29\" width=\"229\" height=\"154\" \/><\/p>\n<p>Question 1.<br \/>\nWhich angle pair is a pair of alternate exterior angles?<br \/>\nOptions:<br \/>\nA. \u22205 and \u22206<br \/>\nB. \u22206 and\u22207<br \/>\nC. \u22205 and \u22204<br \/>\nD. \u22205 and \u22202<\/p>\n<p>Answer:<br \/>\nC. \u22205 and \u22204<\/p>\n<p>Explanation:<br \/>\n\u22205 and \u22204 are alternate exterior angles<\/p>\n<p>Question 2.<br \/>\nWhich of the following angles is not congruent to \u22203?<br \/>\nOptions:<br \/>\nA. \u22201<br \/>\nB. \u22202<br \/>\nC. \u22206<br \/>\nD. \u22208<\/p>\n<p>Answer:<br \/>\nB. \u22202<\/p>\n<p>Explanation:<br \/>\n\u22202 and \u22203 are same-side interior angles. They are not congruent instead their sum is equal to 180\u00b0<\/p>\n<p>Question 3.<br \/>\nThe measures, in degrees, of the three angles of a triangle are given by 2x + 1, 3x &#8211; 3, and 9x. What is the measure of the smallest angle?<br \/>\nOptions:<br \/>\nA. 13\u00b0<br \/>\nB. 27\u00b0<br \/>\nC. 36\u00b0<br \/>\nD. 117\u00b0<\/p>\n<p>Answer:<br \/>\nB. 27\u00b0<\/p>\n<p>Explanation:<br \/>\nFrom the Triangle Sum Theorem, the sum of the angles of the triangle is 180\u00b0<br \/>\nm\u22201 + m\u22202 + m\u22203 = 180\u00b0<br \/>\n(2x + 1)\u00b0 + (3x &#8211; 3)\u00b0 + (9x)\u00b0 = 180\u00b0<br \/>\n2x\u00b0 + 1\u00b0 + 3x\u00b0 &#8211; 3\u00b0 + 9x\u00b0 = 180\u00b0<br \/>\n14x\u00b0 &#8211; 2\u00b0 = 180\u00b0<br \/>\n14x\u00b0 = 178\u00b0<br \/>\nx = 13<br \/>\nSubstitute the value of x to find the m\u22201, m\u22202, and m\u22203<br \/>\nm\u22201 = (2x + 1)\u00b0 = (2(13) + 1)\u00b0 = 27\u00b0<br \/>\nm\u22202 = (3x &#8211; 3)\u00b0 = (3(13) &#8211; 3)\u00b0 = 36\u00b0<br \/>\nm\u22203 = (9x)\u00b0 = (9(13))\u00b0 = 117\u00b0<br \/>\nThe smallest angle is 27\u00b0<\/p>\n<p>Question 4.<br \/>\nWhich is a possible measure of \u2220DCA in the triangle below?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-30.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Mixed Review img 30\" width=\"205\" height=\"147\" \/><br \/>\nOptions:<br \/>\nA. 36\u00b0<br \/>\nB. 38\u00b0<br \/>\nC. 40\u00b0<br \/>\nD 70\u00b0<\/p>\n<p>Answer:<br \/>\nD 70\u00b0<\/p>\n<p>Explanation:<br \/>\nUsing the Exterior Angle Theorem<br \/>\nm\u2220A + m\u2220B = m\u2220DCA<br \/>\nm\u2220A + 40\u00b0 = m\u2220DCA<br \/>\nm\u2220DCA will be greater than 40\u00b0. The only suitable option is D, 70\u00b0.<\/p>\n<p>Question 5.<br \/>\nKaylee wrote in her dinosaur report that the Jurassic period was 1.75 \u00d7 10<sup>8<\/sup> years ago. What is this number written in standard form?<br \/>\nOptions:<br \/>\nA. 1,750,000<br \/>\nB. 17,500,000<br \/>\nC. 175,000,000<br \/>\nD. 17,500,000,000<\/p>\n<p>Answer:<br \/>\nC. 175,000,000<\/p>\n<p>Explanation:<br \/>\n1.75 \u00d7 10<sup>8<\/sup> standard form<br \/>\nMove the decimal point to 8 right places.<br \/>\n175,000,000<\/p>\n<p>Question 6.<br \/>\nGiven that y is proportional to x, what linear equation can you write if y is 16 when x is 20?<br \/>\nOptions:<br \/>\nA. y = 20x<br \/>\nB. y = \\(\\frac{5}{4}\\) x<br \/>\nC. y = \\(\\frac{4}{5}\\)x<br \/>\nD. y = 0.6x<\/p>\n<p>Answer:<br \/>\nC. y = \\(\\frac{4}{5}\\)x<\/p>\n<p>Explanation:<br \/>\nY=4\/5x<br \/>\n16=4\/5(20)<br \/>\n4\/5\u00d720\/1=80\/5<br \/>\n80\/5=16<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 7.<br \/>\nTwo transversals intersect two parallel lines as shown.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-11-Angle-Relationships-in-Parallel-Lines-and-Triangles-img-31.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles Mixed Review img 31\" width=\"190\" height=\"112\" \/><br \/>\na. What is the value of x?<br \/>\nx = ________<\/p>\n<p>Answer:<br \/>\nx = 4<\/p>\n<p>Explanation:<br \/>\n<span id=\"MathJax-Span-149\" class=\"mrow\"><span id=\"MathJax-Span-150\" class=\"mtable\"><span id=\"MathJax-Span-151\" class=\"mtd\"><span id=\"MathJax-Span-152\" class=\"mrow\"><span id=\"MathJax-Span-153\" class=\"mtext\">m<\/span><span id=\"MathJax-Span-154\" class=\"mi\">\u2220<\/span><span id=\"MathJax-Span-155\" class=\"mi\">J<\/span><span id=\"MathJax-Span-156\" class=\"mi\">K<\/span><span id=\"MathJax-Span-157\" class=\"mi\">L = <\/span><\/span><\/span><span id=\"MathJax-Span-158\" class=\"mtd\"><span id=\"MathJax-Span-159\" class=\"mrow\"><span id=\"MathJax-Span-162\" class=\"mtext\">m<\/span><span id=\"MathJax-Span-163\" class=\"mi\">\u2220<\/span><span id=\"MathJax-Span-164\" class=\"mi\">L<\/span><span id=\"MathJax-Span-165\" class=\"mi\">N<\/span><span id=\"MathJax-Span-166\" class=\"mi\">M<br \/>\n<\/span><\/span><\/span><span id=\"MathJax-Span-173\" class=\"mtd\"><span id=\"MathJax-Span-174\" class=\"mrow\"><span id=\"MathJax-Span-175\" class=\"mi\"><\/span><span id=\"MathJax-Span-176\" class=\"mo\">6x + 1 = <\/span><span id=\"MathJax-Span-177\" class=\"mn\">25<br \/>\n<\/span><\/span><\/span><span id=\"MathJax-Span-182\" class=\"mtd\"><span id=\"MathJax-Span-183\" class=\"mrow\"><span id=\"MathJax-Span-184\" class=\"mi\"><\/span><span id=\"MathJax-Span-185\" class=\"mo\">6x = <\/span><span id=\"MathJax-Span-186\" class=\"mn\">24<br \/>\n<\/span><\/span><\/span><span id=\"MathJax-Span-190\" class=\"mtd\"><span id=\"MathJax-Span-191\" class=\"mrow\"><span id=\"MathJax-Span-192\" class=\"mi\"><\/span><span id=\"MathJax-Span-193\" class=\"mo\">x = <\/span><span id=\"MathJax-Span-194\" class=\"mstyle\"><span id=\"MathJax-Span-195\" class=\"mrow\"><span id=\"MathJax-Span-196\" class=\"mn\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Question 7.<br \/>\nb. What is the measure of \u2220LMN?<br \/>\n_________\u00b0<\/p>\n<p>Answer:<br \/>\n23\u00b0<\/p>\n<p>Explanation:<br \/>\nm\u2220LMN = 3x + 11 = 3(4) + 11 = 12 + 11 = 23<\/p>\n<p>Question 7.<br \/>\nc. What is the measure of \u2220KLM?<br \/>\n\u2220KLM = _________\u00b0<\/p>\n<p>Answer:<br \/>\n\u2220KLM = 48\u00b0<\/p>\n<p>Explanation:<br \/>\n\u2220KLM exterior angle of the triangle LMN<br \/>\nm\u2220KLM = m\u2220LNM + m\u2220LMN<br \/>\n= 25 + 23 = 48<\/p>\n<p>Question 7.<br \/>\nd. Which two triangles are similar? How do you know?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\ntriangle JKL = triangle LNM<br \/>\ntriangle KJL = triangle LMN<\/p>\n<p>Explanation:<br \/>\ntriangle JLK and triangle LNM are similar.<br \/>\ntriangle JKL = triangle LNM<br \/>\ntriangle KJL = triangle LMN<\/p>\n<h3>Summary:<\/h3>\n<p>The solutions provided in the Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles are made by the professionals. Practice all the math questions available on the 8th Grade Text Book and learn how to solve the questions in a simple way. Hope the information provided in this article is beneficial for all the students of grade 8. Keep in touch with our website to get the pdfs of all the Go Math Grade 8 Answer Key Chapterwise.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Are you browsing for Go Math Grade 8 Answer Key for Chapter 11 Angle Relationships in Parallel Lines and Triangles on the various websites? Don&#8217;t worry discover all the questions, answers, and explanations on Go Math Grade 8 Solution Key Ch 11 Angle Relationships in Parallel Lines and Triangles here. Get free access to Download &#8230; <a title=\"Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-11-angle-relationships-in-parallel-lines-and-triangles\/\" aria-label=\"More on Go Math Grade 8 Answer Key Chapter 11 Angle Relationships in Parallel Lines and Triangles\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":8784,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/go-math-grade-8-chapter-11-angle-relationships-in-parallel-lines-and-triangles-answer-key.jpeg","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6737"}],"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\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=6737"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6737\/revisions"}],"predecessor-version":[{"id":92794,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6737\/revisions\/92794"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/8784"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=6737"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=6737"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=6737"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}