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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
If g = 11y, a = 4x − y, and d = 5y + 2x − 20, find h.
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09 Mar 2021, 22:25
09 Mar 2021, 22:25
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If g = 11y, a = 4x − y, and d = 5y + 2x − 20, find h where line XY is parallel to line QU.
A. 70°
B. 80°
C. 90°
D. 110°
E. 120°
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
If g = 11y, a = 4x − y, and d = 5y + 2x − 20, find h.
[#permalink]
17 Mar 2021, 02:46
17 Mar 2021, 02:46
Expert Reply
Official Explanation
You are given the measure of one acute angle (a) and one obtuse angle (g). Because any acute angle in this diagram is supplementary to any obtuse angle, then \(11y + 4x − y = 180,\) or \(4x + 10y = 180.\) Because angle d is equal to angle a, then \(5y + 2x − 20 = 4x − y,\) or \(2x − 6y = −20.\) You can set up a system of two equations with two variables:
\(2x-6y=-20\) ------>____\(-4x+12y=40\)
__________________________\(4x+10y=180\)
_____________________________________________
__________________________\(22y=220\)
__________________________\(y=10, x=20\)
h is one of the acute angles, therefore, h has the same measure as a: \(4x − y = 4(20) − 10 = 70.\)
Answer: A
You are given the measure of one acute angle (a) and one obtuse angle (g). Because any acute angle in this diagram is supplementary to any obtuse angle, then \(11y + 4x − y = 180,\) or \(4x + 10y = 180.\) Because angle d is equal to angle a, then \(5y + 2x − 20 = 4x − y,\) or \(2x − 6y = −20.\) You can set up a system of two equations with two variables:
\(2x-6y=-20\) ------>____\(-4x+12y=40\)
__________________________\(4x+10y=180\)
_____________________________________________
__________________________\(22y=220\)
__________________________\(y=10, x=20\)
h is one of the acute angles, therefore, h has the same measure as a: \(4x − y = 4(20) − 10 = 70.\)
Answer: A
gmatclubot
If g = 11y, a = 4x − y, and d = 5y + 2x − 20, find h. [#permalink]
17 Mar 2021, 02:46
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