In the given figure, is a diameter and is a cyclic quadrilateral. If find

Question

Philoid · Accepted Answer

In cyclic quadrilateral PQRS,

∠PSR + ∠PQR = 180°[Opposite angles]

⇒ 150° + ∠PQR = 180°

⇒ ∠PQR = 30°

In triangle PQR,

∠RPQ + ∠PQR + ∠PRQ = 180°[Sum of angles of triangle]

⇒ ∠RPQ + 30° + 90° = 180°

⇒ ∠RPQ + 120° = 180°

⇒ ∠RPQ = 60°