Question

In the given figure, POQ is the diameter of the circle with center O. Quadrilateral PQRS is a cyclic quadrilateral and SQ is joined. If ∠R=138^o, then find ∠PQS.

Answer 1

Given POQ is the diameter of a given circle. PQRS is a cyclic quadrilateral. SQ is joined. Also, ∠SRQ=138^o
∠PSQ=90^∘(angle in a semicircle)
∠QPS+∠QRS=180^o
∠QPS =180^o−∠QRS= 42^o
In △PSQ,
∠PQS +∠PSQ +∠QPS=180^o
∠PQS = 180^o −(∠PSQ+∠QPS)= 48^o