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Question

# In the figure given below, if OP || RS, ∠OPQ = 110o and ∠QRS = 130o, then ∠PQR is equal to

A

60

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B

65

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C

40

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D

45

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Solution

## The correct option is A 60∘ Extend OP. Then, a triangle PQT will be formed; where T is the point at which OP cuts QR. Now, ∠OPQ + ∠QPT = 180∘ ⇒∠QPT = 180∘ - 110∘ = 70∘ Now, since if OP || RS, ∠SRQ and ∠UTQ are corresponding angles hence, ∠UTQ = ∠SRQ = 130∘ Therefore we have, ∠UTQ + ∠PTQ = 180∘ ⇒∠PTQ = 180∘ - 130∘ = 50∘ In triangle PTQ, ∠PTQ + ∠TQP + ∠QPT = 180∘ ⇒50∘ + ∠TQP + 70∘ = 180∘ ⇒∠TQP = 180∘ - 120∘ = 60∘ ⇒∠TQP = ∠PQR = 60∘

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