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Question

PQRS is a cyclic quadrilateral whose diagonals intersect at A. If SQR=80 and QPR=30, then find SRQ.


A
70
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B
60
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C
80
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D
50
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Solution

The correct option is A 70
Given, SQR=80.
Since angles in the same segment are equal, we have
SQR=SPR=80.

But, SPQ=SPR+RPQ=80+30
SPQ=110
Since opposite angles are supplementary in a cyclic quadrilateral, we have
SPQ+SRQ=180.
SRQ=180SPQ=180110=70

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