Question

In the figure, PQ is a diameter of the circle. Angle PQS = $35^\circ$. Find angle QRS.

Accepted Answer

A. Since PQ is the diameter, $\angle PSQ = 90^\circ$ (angle in a semicircle). In $	riangle PSQ$, $\angle QPS = 180^\circ - 90^\circ - 35^\circ = 55^\circ$. Since angles subtended by chord QS in the same segment are equal: $$\angle QRS = \angle QPS = 55^\circ.$$

Angle subtended by chord in circle

Explanation

Practise this under exam conditions