Question

Find the unknown angles x and y in the given figure, where O is the centre of the circle.

Answer 1

According to the theorem, the angle subtended by an arc of the circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

This implies:

$\angle PRQ=\frac{1}{2}\angle POQ$

$x=\frac{120°}{2}=60°$
Also, by the theorem, angles in the same segment of a circle are equal.

Hence, ∠PRQ = ∠PSQ.

So, x = y.

Therefore, y = 60°