Question

In the given figure, POQ is a diameter and
PQRS is a cyclic quadrilateral. If PSR = 150º,
find RPQ.​

Answer 1

Answer:

Given that

POQ is a diameter

PQRS is a cyclic quadrilateral

<PSR=150°

Now,

<PSR+<PQR=180 (Sum of opposite angles of a

cyclic quadrilateral is 180°)

=>150+<PQR=180

=> <PQR=30°

Again,

<PRQ=90° (Angle in a semi circle)

In triangle PQR

<PQR+<PRQ+<RPQ=180 (Angle sum property of

a triangle)

30+90+<RPQ=180

=>120+<RPQ=180

=> <RPQ=60° Ans.