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In the figure above, line l is parallel to line k. Tran
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11 Nov 2020, 10:02
11 Nov 2020, 10:02
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92% (01:32) correct
7% (00:17) wrong based on 41 sessions
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GRE Which of the following angles have measure 40°.jpg [ 29.24 KiB | Viewed 1931 times ]
In the figure above, line \(\ell\) is parallel to line \(k\). Transversals \(m \) and \(n\) intersect at point \(P\) on \(\ell\) and intersect \(k\) at points \(R\) and \(Q\), respectively. Point \(Y\) is on \(k\), points \(S\) and \(T \) are on \(\ell\), the measure of \(∠PRY\) is 140°, and the measure of \(∠QPR\) is 100°. Which of the following angles have measure 40°?
Indicate all such angles.
A. ∠PRQ
B. ∠PQR
C. ∠QPS
D. ∠RPT
Source: 320 GRE Math Questions
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Official Answer
A,B,C,D
Re: In the figure above, line l is parallel to line k. Tran
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25 Nov 2020, 03:07
25 Nov 2020, 03:07
1
Carcass wrote:
Attachment:
GRE Which of the following angles have measure 40°.jpg
In the figure above, line \(\ell\) is parallel to line \(k\). Transversals \(m \) and \(n\) intersect at point \(P\) on \(\ell\) and intersect \(k\) at points \(R\) and \(Q\), respectively. Point \(Y\) is on \(k\), points \(S\) and \(T \) are on \(\ell\), the measure of \(∠PRY\) is 140°, and the measure of \(∠QPR\) is 100°. Which of the following angles have measure 40°?
Indicate all such angles.
A. ∠PRQ
B. ∠PQR
C. ∠QPS
D. ∠RPT
Source: 320 GRE Math Questions
Option A:-- ∠PRQ is on the straight line, so ∠PRQ + 140° = 180°.
∠PRQ = 40°. Option A is getting satisfied.
Option B:-- Sum of all the angles in a triangle should be equal to 180°.
=> 100° + ∠PRQ + ∠PQR = 180°. --> 100° + 40° + ∠PQR = 180°.
∠PQR = 40°. Option B is getting satisfied.
Option C:-- When ∠PQR is 40° then ∠TPN should be 40° because line n is a transversal passing through parallel lines l and k, and based on the transversal rule these two angles should be equal. Also note I am considering n as a point on the extreme upper end of the line n.
If ∠TPN = 40° then ∠QPS should be 40° because they are vertically opposite angles. Hence option C is getting satisfied.
Option D:-- Similarly, when ∠PRQ is 40° then ∠SPM should be 40° because line m is a transversal passing through parallel lines l and k, and based on the transversal rule these two angles should be equal. Also note I am considering m as a point on the extreme upper end of the line m.
If ∠SPM = 40° then ∠RPT should be 40° because they are vertically opposite angles. Hence option D is getting satisfied.
Therefore option A, B, C and D are right answers.
gmatclubot
Re: In the figure above, line l is parallel to line k. Tran [#permalink]
25 Nov 2020, 03:07
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