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Answer: Option A
:
A
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A
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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