In the given figure, PQRS is a cyclic quadrilateral. Its diagonals PR and QS intersect each other at T. If ∠PRS=80∘and∠RQS=50∘, calculate ∠PSR.
A
30∘
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B
50∘
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C
70∘
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D
90∘
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Solution
The correct option is B50∘ Given:PQRSisacyclicquadilateral.∠PRS=80o....(1)∠RQS=50o∠RQS=∠RPS(Anglesinthesamesegmentareequal)⇒∠RPS=50o...(2)In△PSR∠PRS+∠RPS+∠PSR=180o(Anglesumproperty)80o+50o+∠PSR=180o(From(1)and(2))⇒∠PSR=180o−130o∠PSR=50oHenceoption(B)isright