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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
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Question Stats:
91% (01:44) correct
9%
(01:36)
wrong
based on 57
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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°?
I. ∠PQR
II. ∠QPS
III. ∠RPT
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
Attachment:
1.jpg [ 29.24 KiB | Viewed 4010 times ]
16 Dec 2020, 06:38
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Bunuel
Statement I: ∠PRQ = 180 - 40 = 40° Sum of angles on a straight line = 180°
∠PQR = 180 - 100 - 40 = 40°. Sum of angles of a triangle = 180°.
Statement II: ∠PQR = 40°
So ∠PQR = ∠QPS = 40°. Alternate angles between 2 parallel lines cut by a Transversal.
Statement III: ∠PRQ = 40°
So ∠PRQ = ∠RPT = 40°. Alternate angles between 2 parallel lines cut by a Transversal.
All 3 angles = 40°
Option E
Arun Kumar
16 Dec 2020, 08:09
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\(∠PRQ= 40° as 180°-140°\).(Sum of angles on the same line is 180°).
Therefore, \(∠PQR = 40°\) as in triangle PQR, \(∠PRQ=140°\) and \(∠RPQ=100°\).
As sum of angles of a triangle are 180°, \(∠PQR = 40°\)
both angles \(∠QPS and ∠RPT = 40°\) as they are alternate angles to \(∠PRQ\) and \(∠PQR \)which are both equal to \(40°\) (When 2 parallel lines are cut by a Transversal, alternate angles are formed.)
Therefore, the OA is E.
Therefore, \(∠PQR = 40°\) as in triangle PQR, \(∠PRQ=140°\) and \(∠RPQ=100°\).
As sum of angles of a triangle are 180°, \(∠PQR = 40°\)
both angles \(∠QPS and ∠RPT = 40°\) as they are alternate angles to \(∠PRQ\) and \(∠PQR \)which are both equal to \(40°\) (When 2 parallel lines are cut by a Transversal, alternate angles are formed.)
Therefore, the OA is E.
