{"id":70041,"date":"2022-06-17T19:31:05","date_gmt":"2022-06-17T14:01:05","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=70041"},"modified":"2022-05-10T12:58:59","modified_gmt":"2022-05-10T07:28:59","slug":"eureka-math-grade-7-module-6-lesson-1","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-7-module-6-lesson-1\/","title":{"rendered":"Eureka Math Grade 7 Module 6 Lesson 1 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 7th Grade Module 6 Lesson 1 Answer Key<\/h2>\n

Eureka Math Grade 7 Module 6 Lesson 1 Example Answer Key<\/h3>\n

Example 1.
\nThe measures of two supplementary angles are in the ratio of 2:3. Find the measurements of the two angles.
\nAnswer:
\n\"Engage
\n2x + 3x = 180
\n5x = 180
\n(\\(\\frac{1}{5}\\))5x = (\\(\\frac{1}{5}\\))180
\nx = 36
\nAngle 1 = 2(36)\u00b0 = 72\u00b0
\nAngle 2 = 3(36)\u00b0 = 108\u00b0<\/p>\n

Example 2.
\nTwo lines meet at a point that is also the vertex of an angle. Set up and solve an appropriate equation for x and y.
\n\"Engage
\nAnswer:
\n16 + y = 90 Complementary angles
\n16 – 16 + y = 90-16
\ny = 74<\/p>\n

x + (74) = 180 Supplementary angles
\nx + 74 – 74 = 180 – 74
\nx = 106<\/p>\n

Eureka Math Grade 7 Module 6 Lesson 1 Exercise Answer Key<\/h3>\n

Exercise 1.
\nIn a complete sentence, describe the relevant angle relationships in the diagram. Write an equation for the angle relationship shown in the figure and solve for x. Confirm your answers by measuring the angle with a protractor.
\n\"Engage
\nAnswer:
\nThe angles x\u00b0 and 22\u00b0 are supplementary and sum to 180\u00b0.
\nx + 22 = 180
\nx + 22 – 22 = 180 – 22
\nx = 158
\nThe measure of the angle is 158\u00b0.<\/p>\n

Exercise 2.
\nIn a pair of complementary angles, the measurement of the larger angle is three times that of the smaller angle. Find the measurements of the two angles.
\nAnswer:
\nx + 3x = 90
\n4x = 90
\n(\\(\\frac{1}{4}\\))4x = (\\(\\frac{1}{4}\\))90
\nx = 22.5
\nAngle 1 = 22.5\u00b0
\nAngle 2 = 3(22.5)\u00b0 = 67.5\u00b0<\/p>\n

Exercise 3.
\nThe measure of a supplement of an angle is 6\u00b0 more than twice the measure of the angle. Find the measurement of the two angles.
\nAnswer:
\nx + (2x + 6) = 180
\n3x + 6 = 180
\n3x + 6 – 6 = 180 – 6
\n3x = 174
\n(\\(\\frac{1}{3}\\))3x = (\\(\\frac{1}{3}\\))174
\nx = 58
\nAngle 1 = 58\u00b0
\nAngle 2 = 2(58)\u00b0 + 6\u00b0 = 122\u00b0<\/p>\n

Exercise 4.
\nThe measure of a complement of an angle is 32\u00b0 more than three times the angle. Find the measurement of the two angles.
\nAnswer:
\nx + (3x + 32) = 90
\n4x + 32 – 32 = 90 – 32
\n4x = 58
\n(\\(\\frac{1}{4}\\))4x = (\\(\\frac{1}{4}\\))58
\nx = 14.5
\nAngle 1 = 14.5\u00b0
\nAngle 2 = 3(14.5)\u00b0 + 32\u00b0 = 75.5\u00b0<\/p>\n

Scaffolding solutions:
\na. The x\u00b0 angle and the 22\u00b0 angle are supplementary and sum to 180\u00b0.
\nb. x + 22 = 180
\nc. The equation shows that an unknown value, x (which is the unknown angle in the diagram) plus 22 is equal to 180. The 22 represents the angle that we know, which is 22 degrees.
\nd.
\nx + 22 = 180
\nx + 22 – 22 = 180 – 22
\nx = 158
\nx = 158 means that in the diagram, the missing angle measures 158\u00b0.
\nThe answer of 158\u00b0 is correct. If we substitute 158 for x, we get 158 + 22 = 180, which is a true number sentence. This is reasonable because when we look at the diagram, we would expect the angle to be obtuse.<\/p>\n

Eureka Math Grade 7 Module 6 Lesson 1 Problem Set Answer Key<\/h3>\n

Question 1.
\nTwo lines meet at a point that is also the endpoint of a ray. Set up and solve the appropriate equations to determine x and y.
\n\"Eureka
\nAnswer:
\nx + 55 = 90 Complementary angles
\nx + 55 – 55 = 90 – 55
\nx = 35<\/p>\n

55 + y = 180 Supplementary angles
\n55 – 55 + y = 180 – 55
\ny = 125<\/p>\n

Question 2.
\nTwo lines meet at a point that is also the vertex of an angle. Set up and solve the appropriate equations to determine x and y.
\n\"Eureka
\nAnswer:
\ny + x = 90 Complementary angles<\/p>\n

x + 32 = 90 Complementary angles
\nx + 32 – 32 = 90 – 32
\nx = 58<\/p>\n

y + (58) = 90 Complementary angles
\ny + 58 – 58 = 90 – 58
\ny = 32<\/p>\n

Question 3.
\nTwo lines meet at a point that is also the vertex of an angle. Set up and solve an appropriate equation for x and y.
\n\"Eureka
\nAnswer:
\nx + y = 180 Supplementary angles<\/p>\n

28 + y = 90 Complementary angles
\n28 – 28 + y = 90 – 28
\ny = 62<\/p>\n

x + (62) = 180 Supplementary angles
\nx + 62-62 = 180 – 62
\nx = 118<\/p>\n

Question 4.
\nSet up and solve the appropriate equations for s and t.
\n\"Eureka
\nAnswer:
\n79 + t = 90 Complementary angles
\n79 – 79 + t = 90 – 79
\nt = 11<\/p>\n

19 + (11) + 79 + s = 180 Angles on a line
\n109 + s = 180
\n109 – 109 + s = 180 – 109
\ns = 71<\/p>\n

Question 5.
\nTwo lines meet at a point that is also the endpoint of two rays. Set up and solve the appropriate equations for m and n.
\n\"Eureka
\nAnswer:
\n43 + m = 90 Complementary angles
\n43-43 + m = 90-43
\nm = 47<\/p>\n

38 + 43 + (47) + n = 180 Angles on a line
\n128 + n = 180
\n128-128 + n = 180-128
\nn = 52<\/p>\n

Question 6.
\nThe supplement of the measurement of an angle is 16\u00b0 less than three times the angle. Find the measurement of the angle and its supplement.
\nAnswer:
\nx + (3x-16) = 180
\n4x-16 + 16 = 180 + 16
\n4x = 196
\n(\\(\\frac{1}{4}\\))4x = (\\(\\frac{1}{4}\\))196
\nx = 49
\nAngle = 49\u00b0
\nSupplement = 3(49)\u00b0-16\u00b0 = 131\u00b0<\/p>\n

Question 7.
\nThe measurement of the complement of an angle exceeds the measure of the angle by 25%. Find the measurement of the angle and its complement.
\nAnswer:
\nx + (x + \\(\\frac{1}{4}\\) x) = 90
\nx + \\(\\frac{5}{4}\\) x = 90
\n\\(\\frac{9}{4}\\)x = 90
\n(\\(\\frac{4}{9}\\)) \\(\\frac{9}{4}\\)x = (\\(\\frac{4}{9}\\))90
\nx = 40
\nAngle = 40\u00b0
\nComplement = \\(\\frac{5}{4}\\)(40)\u00b0 = 50\u00b0<\/p>\n

Question 8.
\nThe ratio of the measurement of an angle to its complement is 1:2. Find the measurement of the angle and its complement.
\nAnswer:
\nx + 2x = 90
\n3x = 90
\n(\\(\\frac{1}{3}\\))3x = (\\(\\frac{1}{3}\\))90
\nx = 30
\nAngle = 30\u00b0
\nComplement = 2(30)\u00b0 = 60\u00b0<\/p>\n

Question 9.
\nThe ratio of the measurement of an angle to its supplement is 3:5. Find the measurement of the angle and its supplement.
\nAnswer:
\n3x + 5x = 180
\n8x = 180
\n(\\(\\frac{1}{8}\\))8x = (\\(\\frac{1}{8}\\))180
\nx = 22.5
\nAngle = 3(22.5)\u00b0 = 67.5\u00b0
\nSupplement = 5(22.5)\u00b0 = 112.5\u00b0<\/p>\n

Question 10.
\nLet x represent the measurement of an acute angle in degrees. The ratio of the complement of x to the supplement of x is 2:5. Guess and check to determine the value of x. Explain why your answer is correct.
\nAnswer:
\nSolutions will vary; x = 30\u00b0.
\nThe complement of 30\u00b0 is 60\u00b0. The supplement of 30\u00b0 is 150\u00b0. The ratio of 60 to 150 is equivalent to 2:5.<\/p>\n

Eureka Math Grade 7 Module 6 Lesson 1 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nSet up and solve an equation for the value of x. Use the value of x and a relevant angle relationship in the diagram to determine the measurement of \u2220EAF.
\n\"Eureka
\nAnswer:
\nx + 63 = 90
\nx + 63 – 63 = 90 – 63
\nx = 27
\n\u2220CAG and \u2220EAF are the complements of 63\u00b0. The measurement of \u2220CAG is 27\u00b0; therefore, the measurement of \u2220EAF is also 27\u00b0.<\/p>\n

Question 2.
\nThe measurement of the supplement of an angle is 39\u00b0 more than half the angle. Find the measurement of the angle and its supplement.
\nAnswer:
\nx + (\\(\\frac{1}{2}\\)x + 39) = 180
\n1.5x + 39 = 180
\n1.5x + 39 – 39 = 180 – 39
\n1.5x = 141
\n1.5x \u00f7 1.5 = 141 \u00f7 1.5
\nx = 94
\nThe measurement of the angle is 94\u00b0.
\nThe measurement of the supplement is \\(\\frac{1}{2}\\)(94)\u00b0 + 39\u00b0 = 86\u00b0.
\nOR
\nx + (\\(\\frac{1}{2}\\)x + 39) = 180
\n\\(\\frac{3}{2}\\)x + 39 = 180
\n\\(\\frac{3}{2}\\)x + 39 – 39 = 180 – 39
\n\\(\\frac{3}{2}\\)x = 141
\n(\\(\\frac{2}{3}\\))(\\(\\frac{3}{2}\\)x) = (\\(\\frac{2}{3}\\))141
\nx = 94
\nThe measurement of the angle is 94\u00b0.
\nThe measurement of the supplement is \\(\\frac{1}{2}\\)(94)\u00b0 + 39\u00b0 = 86\u00b0.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 7th Grade Module 6 Lesson 1 Answer Key Eureka Math Grade 7 Module 6 Lesson 1 Example Answer Key Example 1. The measures of two supplementary angles are in the ratio of 2:3. Find the measurements of the two angles. Answer: 2x + 3x = 180 5x = 180 ()5x = … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/70041"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=70041"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/70041\/revisions"}],"predecessor-version":[{"id":137966,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/70041\/revisions\/137966"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=70041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=70041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=70041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}