{"id":82497,"date":"2021-04-01T18:30:13","date_gmt":"2021-04-01T13:00:13","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=82497"},"modified":"2022-04-01T10:26:06","modified_gmt":"2022-04-01T04:56:06","slug":"eureka-math-grade-8-module-2-lesson-14","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/eureka-math-grade-8-module-2-lesson-14\/","title":{"rendered":"Eureka Math Grade 8 Module 2 Lesson 14 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 8th Grade Module 2 Lesson 14 Answer Key<\/h2>\n

Eureka Math Grade 8 Module 2 Lesson 14 Example Answer Key<\/h3>\n

Example 1
\nFind the measure of angle x.
\n\"Engage
\nAnswer:
\nWe need to find the sum of the measures of the remote interior angles to find the measure of the exterior angle x:
\n14+30=44. Therefore, the measure of \u2220x is 44\u00b0.<\/p>\n

\u2192 Present an informal argument that proves you are correct.
\n\u2192 We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220ABC must be 136\u00b0, which means that \u2220x is 44\u00b0.<\/p>\n

Example 2.
\nFind the measure of angle x.
\n\"Engage
\nAnswer:
\nWe need to find the sum of the measures of the remote interior angles to find the measure of the exterior angle x: 44+32=76. Therefore, the measure of \u2220x is 76\u00b0.<\/p>\n

\u2192 Present an informal argument that proves you are correct.
\n\u2192 We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220ACB must be 104\u00b0, which means that \u2220x is 76\u00b0.<\/p>\n

Example 3.
\nFind the measure of angle x.
\n\"Engage
\nAnswer:
\n180-121=59. Therefore, the measure of \u2220x is 59\u00b0.<\/p>\n

Students should notice that they are not given the two remote interior angles associated with the exterior angle x.
\nFor that reason, they must use what they know about straight angles (or supplementary angles) to find the measure of
\nangle x.<\/p>\n

Example 4.
\nFind the measure of angle x.
\n\"Engage
\nAnswer:
\n129-45=84. Therefore, the measure of \u2220x is 84\u00b0.<\/p>\n

Eureka Math Grade 8 Module 2 Lesson 14 Exercise Answer Key<\/h3>\n

Exercises 1\u20134
\nUse the diagram below to complete Exercises 1\u20134.
\n\"Eureka<\/p>\n

Exercise 1.
\nName an exterior angle and the related remote interior angles.
\nAnswer:
\nThe exterior angle is \u2220ZYP, and the related remote interior angles are \u2220YZX and \u2220ZXY.<\/p>\n

Exercise 2.
\nName a second exterior angle and the related remote interior angles.
\nAnswer:
\nThe exterior angle is \u2220XZQ, and the related remote interior angles are \u2220ZYX and \u2220ZXY.<\/p>\n

Exercise 3.
\nName a third exterior angle and the related remote interior angles.
\nAnswer:
\nThe exterior angle is \u2220RXY, and the related remote interior angles are \u2220ZYX and \u2220XZY.<\/p>\n

Exercise 4.
\nShow that the measure of an exterior angle is equal to the sum of the measures of the related remote interior angles.
\nAnswer:
\nTriangle XYZ has interior angles \u2220XYZ, \u2220YZX, and \u2220ZXY. The sum of those angles is 180\u00b0. The straight angle \u2220XYP also has a measure of 180\u00b0 and is made up of angles \u2220XYZ and \u2220ZYP. Since the triangle and the straight angle have the same number of degrees, we can write the sum of their respective angles as an equality:
\n\u2220XYZ+\u2220YZX+\u2220ZXY=\u2220XYZ+ZYP.
\nBoth the triangle and the straight angle share \u2220XYZ. We can subtract the measure of that angle from the triangle and the straight angle. Then, we have
\n\u2220YZX+\u2220ZXY=\u2220ZYP,
\nwhere the angle \u2220ZYP is the exterior angle, and the angles \u2220YZX and \u2220ZXY are the related remote interior angles of the triangle. Therefore, the sum of the measures of the remote interior angles of a triangle are equal to the measure of the exterior angle.<\/p>\n

Exercise 5\u201310<\/p>\n

Question 5.
\nFind the measure of angle x. Present an informal argument showing that your answer is correct.
\n\"Eureka
\nAnswer:
\nSince 89+28 = 117, the measure of angle x is 117\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220ACB must be 63\u00b0, which means that \u2220x is 117\u00b0.<\/p>\n

Question 6.
\nFind the measure of angle x. Present an informal argument showing that your answer is correct.
\n\"Eureka
\nAnswer:
\nSince 59+52=111, the measure of angle x is 111\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220CAB must be 69\u00b0, which means that \u2220x is 111\u00b0.<\/p>\n

Question 7.
\nFind the measure of angle x. Present an informal argument showing that your answer is correct.
\n\"Eureka
\nAnswer:
\nSince 180-79=101, the measure of angle x is 101\u00b0. We know that straight angles are 180\u00b0, and the straight angle in the diagram is made up of \u2220ABC and \u2220x. \u2220ABC is 79\u00b0, which means that \u2220x is 101\u00b0.<\/p>\n

Question 8.
\nFind the measure of angle x. Present an informal argument showing that your answer is correct.
\n\"Eureka
\nAnswer:
\nSince 71+74=145, the measure of angle x is 145\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220ACB must be 35\u00b0, which means that \u2220x is 145\u00b0.<\/p>\n

Question 9.
\nFind the measure of angle x. Present an informal argument showing that your answer is correct.
\n\"Eureka
\nAnswer:
\nSince 107+32=139, the measure of angle x is 139\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220CBA must be 41\u00b0, which means that x is 139\u00b0.<\/p>\n

Question 10.
\nFind the measure of angle x. Present an informal argument showing that your answer is correct.
\n\"Eureka
\nAnswer:
\nSince 156-81 = 75, the measure of angle x is 75\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220BAC must be 24\u00b0 because it is part of the straight angle. Then, \u2220x=180\u00b0-(81\u00b0+24\u00b0), which means \u2220x is 75\u00b0.<\/p>\n

Eureka Math Grade 8 Module 2 Lesson 14 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nFind the measure of angle p. Present an informal argument showing that your answer is correct.
\n\"Engage
\nAnswer:
\nThe measure of angle p is 67\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220BAC must be 113\u00b0, which means that \u2220p is 67\u00b0.<\/p>\n

Question 2.
\nFind the measure of angle q. Present an informal argument showing that your answer is correct.
\n\"Engage
\nAnswer:
\nThe measure of angle q is 27\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220CAB must be 25\u00b0, which means that \u2220q is 27\u00b0.<\/p>\n

Question 3.
\nFind the measure of angle r. Present an informal argument showing that your answer is correct.
\n\"Engage
\nAnswer:
\nThe measure of angle r is 121\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220BCA must be 59\u00b0, which means that \u2220r is 121\u00b0.<\/p>\n

Eureka Math Grade 8 Module 2 Lesson 14 Problem Set Answer Key<\/h3>\n

Students practice finding missing angle measures of triangles.<\/p>\n

For each of the problems below, use the diagram to find the missing angle measure. Show your work.<\/p>\n

Question 1.
\nFind the measure of angle x. Present an informal argument showing that your answer is correct.
\n\"Eureka
\nAnswer:
\nSince 26+13=39, the measure of angle x is 39\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220BCA must be 141\u00b0, which means that \u2220x is 39\u00b0.<\/p>\n

Question 2.
\nFind the measure of angle x.
\n\"Eureka
\nAnswer:
\nSince 52+44=96, the measure of angle x is 96\u00b0.<\/p>\n

Question 3.
\nFind the measure of angle x. Present an informal argument showing that your answer is correct.
\n\"Eureka
\nAnswer:
\nSince 76-25=51, the measure of \u2220x is 51\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0. \u2220BAC must be 104\u00b0 because it is part of the straight angle. Then, x=180\u00b0-(104\u00b0+25\u00b0), which means \u2220x is 51\u00b0.<\/p>\n

Question 4.
\nFind the measure of angle x.
\n\"Eureka
\nAnswer:
\nSince 27+52 =79, the measure of angle x is 79\u00b0.<\/p>\n

Question 5.
\nFind the measure of angle x.
\n\"Eureka
\nAnswer:
\nSince 180-104=76, the measure of angle x is 76\u00b0.<\/p>\n

Question 6.
\nFind the measure of angle x.
\n\"Eureka
\nAnswer:
\nSince 52+53=105, the measure of angle x is 105\u00b0.<\/p>\n

Question 7.
\nFind the measure of angle x.
\n\"Eureka
\nAnswer:
\nSince 48+83=131, the measure of angle x is 131\u00b0.<\/p>\n

Question 8.
\nFind the measure of angle x.
\n\"Eureka
\nAnswer:
\nSince 100+26=126, the measure of angle x is 126\u00b0.<\/p>\n

Question 9.
\nFind the measure of angle x.
\n\"Eureka
\nAnswer:
\nSince 126-47=79, the measure of angle x is 79\u00b0.<\/p>\n

Question 10.
\nWrite an equation that would allow you to find the measure of angle x. Present an informal argument showing that your answer is correct.
\n\"Eureka
\nAnswer:
\nSince y+z=x, the measure of angle x is (y+z)\u00b0. We know that triangles have a sum of interior angles that is equal to 180\u00b0. We also know that straight angles are 180\u00b0.
\nThen, \u2220y+\u2220z+\u2220BAC=180\u00b0, and \u2220x+\u2220BAC=180\u00b0. Since both equations are equal to 180\u00b0,
\nthen \u2220y+\u2220z+\u2220BAC=\u2220x+\u2220BAC. Subtract \u2220BAC from each side of the equation, and you get \u2220y+\u2220z=\u2220x.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 8th Grade Module 2 Lesson 14 Answer Key Eureka Math Grade 8 Module 2 Lesson 14 Example Answer Key Example 1 Find the measure of angle x. Answer: We need to find the sum of the measures of the remote interior angles to find the measure of the exterior angle x: … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/82497"}],"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\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=82497"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/82497\/revisions"}],"predecessor-version":[{"id":91543,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/82497\/revisions\/91543"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=82497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=82497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=82497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}