Question 146

In the given figure, POQ is a diameter and PQRS is a cyclic quadrilateral. If ∠PSR = 130°, then the value of ∠RPQ is

Solution

As we know that it is a cyclic quadrilateral , then all points P, Q R ,S are on circumferene of ceircle

we know sum of opposite angles in cyclic quad. = 180

Hence , ∠P + ∠R = 180

∠S + ∠Q = 180

∠S = 130 , so ∠Q = 50

If PQ is a diameter , then ∠PRQ = 90

Sum of angles in a traingle = 180

Hence ∠RPQ = 180 - (90+50) = 40

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