Question

POQ is a diameter and PQRS is a cyclic quadrilateral.If anglePSR=150°,find angle RPQ

Answer 1

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Answer 2

Answer: ∠RPQ is 60°

Step-by-step explanation:

Given : ∠PSR = 150°

PQ is diameter

To find : ∠RPQ

As PQ is diameter

Now  as we know  Angle is semicircle is 90°

Therefore ∠PRQ= 90°

PQRS is a cyclic quadrilateral

the sum of opposite angles of a cyclic quadrilateral is 180°

Therefore

∠PSR+∠PQR= 180°

⇒150°+∠PQR=180°

⇒∠PQR= 30°

Now in Δ PRQ

The angle sum property (the sum of all angles of a triangle is 180°)

∠PQR+∠PRQ+∠RPQ=180°

⇒30°+90°+∠RPQ=180°

⇒∠RPQ=180°-120°

⇒∠RPQ=60°

Hence, the ∠RPQ is 60°