{"id":70131,"date":"2021-03-24T19:31:52","date_gmt":"2021-03-24T14:01:52","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=70131"},"modified":"2022-04-01T10:27:40","modified_gmt":"2022-04-01T04:57:40","slug":"eureka-math-grade-7-module-6-lesson-2","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/eureka-math-grade-7-module-6-lesson-2\/","title":{"rendered":"Eureka Math Grade 7 Module 6 Lesson 2 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 7th Grade Module 6 Lesson 2 Answer Key<\/h2>\n

Eureka Math Grade 7 Module 6 Lesson 2 Example Answer Key<\/h3>\n

Example 1.
\nTwo lines meet at a point that is also the endpoint of a ray. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of p and r.
\n\"Engage
\nAnswer:
\nThe angle r\u00b0 is vertically opposite from and equal to the sum of the angles with measurements 28\u00b0 and 16\u00b0, or a sum of 44\u00b0. Angles r\u00b0 and p\u00b0 are angles on a line and sum to 180\u00b0.
\nr = 28 + 16
\nr = 44\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Vert. \u2220s
\np + (44) = 180
\np + 44 – 44 = 180 – 44
\np = 136\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2220s on a line<\/p>\n

Example 2.
\nThree lines meet at a point. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of z.
\n\"Engage
\nAnswer:
\nLet y\u00b0 be the angle vertically opposite and equal in measurement to 19\u00b0.
\nThe angles z\u00b0 and y\u00b0 are complementary and sum to 90\u00b0.
\nz + y = 90
\nz + 19 = 90
\nz + 19 – 19 = 90 – 19
\nz = 71 Complementary \u2220s<\/p>\n

Example 3.
\nTwo lines meet at a point that is also the endpoint of a ray. The ray is perpendicular to one of the lines as shown. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of t.
\n\"Engage
\nAnswer:
\nThe measurement of the angle formed by adjacent angles of 26\u00b0 and 90\u00b0 is the sum of the adjacent angles. This angle is vertically opposite and equal in measurement to the angle t\u00b0.
\nLet y\u00b0 be the measure of the indicated angle.
\ny = 116\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2220s add
\nt = (y)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Vert.\u2220s
\nt = 116<\/p>\n

Example 4.
\nThree lines meet at a point. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Is your answer reasonable? Explain how you know.
\n\"Engage
\nAnswer:
\nThe angle x\u00b0 is vertically opposite from the angle formed by the right angle that contains and shares a common side with an 8\u00b0 angle.
\nx = 90 – 8\u00a0 \u00a0 \u00a0 \u00a0 \u2220s add and vert.\u2220s
\nx = 82
\nThe answer is reasonable because the angle marked by x\u00b0 is close to appearing as a right angle.<\/p>\n

Eureka Math Grade 7 Module 6 Lesson 2 Exercise Answer Key<\/h3>\n

Exercise 1.
\nThree lines meet at a point. In a complete sentence, describe the relevant angle relationship in the diagram. Set up and solve an equation to find the value of a.
\n\"Engage
\nAnswer:
\nThe two a\u00b0 angles and the angle 144\u00b0 are angles on a line and sum to 180\u00b0.
\n2a + 144 = 180
\n2a + 144-144 = 180 – 144
\n2a = 36
\na = 18\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2220s on a line<\/p>\n

Exercise 2.
\nThree lines meet at a point; \u2220AOF = 144\u00b0. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to determine the value of c.
\n\"Engage
\nAnswer:
\n\u2220EOB, formed by adjacent angles \u2220EOC and \u2220COB, is vertical to and equal in measurement to \u2220AOF.
\nThe measurement of \u2220EOB is c\u00b0 + 90\u00b0 (\u2220s add).
\nc + 90 = 144
\nc + 90 – 90 = 144 – 90
\nc = 54\u00a0 \u00a0 \u00a0 \u00a0 Vert. \u2220s<\/p>\n

Exercise 3.
\nTwo lines meet at a point that is also the endpoint of a ray. The ray is perpendicular to one of the lines as shown. In a complete sentence, describe the relevant angle relationships in the diagram. You may add labels to the diagram to help with your description of the angle relationship. Set up and solve an equation to find the value of v.
\n\"Engage
\nAnswer:
\nOne possible response: Let x\u00b0 be the angle vertically opposite and equal in measurement to 46\u00b0. The angles x\u00b0 and v\u00b0 are adjacent angles, and the angle they form together is equal to the sum of their measurements.
\nx = 46\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Vert.\u2220s
\nv = 90 + 46\u00a0 \u00a0 \u00a0 \u00a0 \u2220s add
\nv = 136<\/p>\n

Exercise 4.
\nTwo lines meet at a point that is also the endpoint of two rays. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Find the measurements of \u2220AOB and \u2220BOC.
\n\"Engage
\nAnswer:
\n\u2220AOC is vertically opposite from the angle formed by adjacent angles 90\u00b0 and 25\u00b0.
\n2x + 3x = 90 + 25
\n5x = 115
\nx = 23\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2220s add and vert.\u2220s<\/p>\n

\u2220AOC = 2(23)\u00b0 = 46\u00b0
\n\u2220BOC = 3(23)\u00b0 = 69\u00b0<\/p>\n

Exercise 5.
\na. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Find the measurements of \u2220AOB and\u2220BOC.
\n\"Engage
\nb. Katrina was solving the problem above and wrote the equation 7x + 20 = 90. Then, she rewrote this as 7x + 20 = 70 + 20. Why did she rewrite the equation in this way? How does this help her to find the value of x?
\nAnswer:
\na. \u2220AOB and \u2220BOC are complementary and sum to 90\u00b0.
\n5x + (2x + 20) = 90\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 complementary \u2220s
\n7x + 20 = 90
\n7x + 20-20 = 90 – 20
\n7x = 70
\nx = 10
\n\u2220AOB = 5(10)\u00b0 = 50\u00b0
\n\u2220BOC = 2(10)\u00b0 + 20\u00b0 = 40\u00b0<\/p>\n

b. She grouped the quantity on the right-hand side of the equation similarly to that of the left-hand side. This way, it is clear that the quantity 7x on the left-hand side must be equal to the quantity 70 on the right-hand side.<\/p>\n

Eureka Math Grade 7 Module 6 Lesson 2 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 an equation to find the value of c.
\n\"Eureka
\nAnswer:
\nc + 90 + 17 = 180 \u2220s on a line
\nc + 107 = 180
\nc + 107 – 107 = 180 – 107
\nc = 73
\nScaffolded solutions:
\na. Use the equation above.
\nb. The angle marked c\u00b0, the right angle, and the angle with measurement 17\u00b0 are angles on a line, and their measurements sum to 180\u00b0.
\nc. Use the solution above. The answer seems reasonable because it looks like it has a measurement a little less than a 90\u00b0 angle.<\/p>\n

Question 2.
\nTwo lines meet at a point that is also the endpoint of a ray. Set up and solve an equation to find the value of a. Explain why your answer is reasonable.
\n\"Eureka
\nAnswer:
\na + 33 = 49\u00a0 \u00a0 \u00a0\u2220s add and vert.\u2220s
\na + 33 – 33 = 49 – 33
\na = 16
\nThe answers seem reasonable because a rounded value of a as 20 and a rounded value of its adjacent angle 33 as 30 yields a sum of 50, which is close to the rounded value of the measurement of the vertical angle.<\/p>\n

Question 3.
\nTwo lines meet at a point that is also the endpoint of a ray. Set up and solve an equation to find the value of w.
\n\"Eureka
\nAnswer:
\nw + 90 = 125 \u2220s add and vert.\u2220s
\nw + 90-90 = 125 – 90
\nw = 35<\/p>\n

Question 4.
\nTwo lines meet at a point that is also the vertex of an angle. Set up and solve an equation to find the value of m.
\n\"Eureka
\nAnswer:
\n(90 – 68) + 24 = m \u2220s add and vert.\u2220s
\nm = 46<\/p>\n

Question 5.
\nThree lines meet at a point. Set up and solve an equation to find the value of r.
\n\"Eureka
\nAnswer:
\nr + 122 + 34 = 180 \u2220s on a line and vert.\u2220s
\nr + 156 = 180
\nr + 156 – 156 = 180 – 156
\nr = 24<\/p>\n

Question 6.
\nThree lines meet at a point that is also the endpoint of a ray. Set up and solve an equation to find the value of each variable in the diagram.
\n\"Eureka
\nAnswer:
\nv = 90-51 Complementary \u2220s
\nv = 39<\/p>\n

w + 39 + 51 + 43 = 180\u00a0 \u00a0 \u00a0 \u00a0 \u2220s on a line
\nw + 133 = 180
\nw + 133 – 133 = 180 – 133
\nw = 47<\/p>\n

x = 51 + 43\u00a0 \u00a0Vert.\u2220s
\nx = 94<\/p>\n

y = 39\u00a0 \u00a0 \u00a0 \u00a0Vert.\u2220s<\/p>\n

z = 47\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Vert.\u2220s<\/p>\n

Question 7.
\nSet up and solve an equation to find the value of x. Find the measurement of \u2220AOB and of \u2220BOC.
\n\"Eureka
\nAnswer:
\n(2x – 15) + 11x = 180\u00a0 \u00a0 \u00a0 Supplementary \u2220s
\n13x – 15 = 180
\n13x – 15 + 15 = 180 + 15
\n13x = 195
\nx = 15
\nThe measurement of \u2220AOB: 2(15)\u00b0 – 15\u00b0 = 15\u00b0
\nThe measurement of \u2220BOC: 11(15)\u00b0 = 165\u00b0
\nScaffolded solutions:
\na. Use the equation above.
\nb. The marked angles are angles on a line, and their measurements sum to 180\u00b0.
\nc. Once 15 is substituted for x, then the measurement of \u2220AOB is 15\u00b0 and the measurement of \u2220BOC is 165\u00b0. These answers seem reasonable since \u2220AOB is acute and \u2220BOC is obtuse.<\/p>\n

Question 8.
\nSet up and solve an equation to find the value of x. Find the measurement of \u2220AOB and of \u2220BOC.
\n\"Eureka
\nAnswer:
\nx + 8 + 2x = 90\u00a0 \u00a0 \u00a0 \u00a0Complementary \u2220s
\n3x + 8 = 90
\n3x + 8-8 = 90-8
\n3x = 82
\nx = 27\\(\\frac{1}{3}\\)
\nThe measurement of \u2220AOB: (27\\(\\frac{1}{3}\\))\u00b0 + 8\u00b0 = 35\\(\\frac{1}{3}\\)\u00b0
\nThe measurement of \u2220BOC: 2(27\\(\\frac{1}{3}\\))\u00b0 = 54\\(\\frac{2}{3}\\)\u00b0<\/p>\n

Question 9.
\nSet up and solve an equation to find the value of x. Find the measurement of \u2220AOB and of \u2220BOC.
\n\"Eureka
\nAnswer:
\n4x + 5 + 5x + 22 = 180\u00a0 \u00a0\u2220s on a line
\n9x + 27 = 180
\n9x + 27-27 = 180-27
\n9x = 153
\nx = 17
\nThe measurement of \u2220AOB: 4(17)\u00b0 + 5\u00b0 = 73\u00b0
\nThe measurement of \u2220BOC: 5(17)\u00b0 + 22\u00b0 = 107\u00b0<\/p>\n

Question 10.
\nWrite a verbal problem that models the following diagram. Then, solve for the two angles.
\n\"Eureka
\nAnswer:
\nOne possible response: Two angles are supplementary. The measurement of one angle is five times the measurement of the other. Find the measurements of both angles.
\n10x + 2x = 180
\n12x = 180
\nx = 15\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Supplementary \u2220s
\nThe measurement of Angle 1: 10(15)\u00b0 = 150\u00b0
\nThe measurement of Angle 2: 2(15)\u00b0 = 30\u00b0<\/p>\n

Eureka Math Grade 7 Module 6 Lesson 2 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nTwo lines meet at a point that is also the vertex of an angle. Set up and solve an equation to find the value of x. Explain why your answer is reasonable.
\n\"Eureka
\nAnswer:
\n65 + (90-27) = x
\nx = 128
\nOR
\ny + 27 = 90
\ny + 27 – 27 = 90 – 27
\ny = 63
\n65 + y = x
\n65 + (63) = x
\nx = 128
\nThe answers seem reasonable because a rounded value of y as 60 and a rounded value of its adjacent angle 65 as 70 yields a sum of 130, which is close to the calculated answer.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 7th Grade Module 6 Lesson 2 Answer Key Eureka Math Grade 7 Module 6 Lesson 2 Example Answer Key Example 1. Two lines meet at a point that is also the endpoint of a ray. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve … 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\/70131"}],"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=70131"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/70131\/revisions"}],"predecessor-version":[{"id":92201,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/70131\/revisions\/92201"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=70131"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=70131"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=70131"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}