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Q.

What is the value of PQR if  PQRSis cyclic quadrilateral and PS = SR?

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a

40°

b

70°

c

90°

d

30°

answer is B.

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Detailed Solution

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Concept: Every angle of a cyclic quadrilateral is on a circle (circumscribed circle), and the sum of any two opposite angles of a cyclic quadrilateral is 180˚.

Since angles opposite to equal sides are equal,

In  ΔPSR,PS=PRPRS=SPR=20°By angle sum property of triangle,

Now,  PSR+SPR+SRP=180°

PSR+20°+20°=180°

PSR=140°

Here,  PQRS is a cyclic quadrilateral.

PQR+PSR=180°PQR=40°

Then, sum of any pair of opposite angles of cyclic quadrilateral is180°.

Hence, the value of PQR=40°

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