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Question

Question 7
In the figure, OP||RS, OPQ=110 and QRS=130, then PQR is equal to:


A) 40
B) 50
C) 60
​​​​​​​D) 70

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Solution

The answer is C.
In the given figure, producing OP, to intersect RQ at X. Since, OP ∥RS and RX is a transversal.

So, RXP=XRS [alternate angles]

RXP=130 [ QRS=130(given)].....(i)
Now, RQ is all line segment.
So, PXQ+RXP=180 [line pair axiom]
PXQ=180RXP=180130 [From Eq. (i)]
PXQ=50
In ΔPQX, OPQ is an exterior angle,
OPQ=PXQ+PQX
[ exterior angle = sum of two opposite interior angles]
110=50+PQX
PQX=11050
PQR=60 [ PQX=PQR]

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