Prove that angles in the same segment of a circle are equal.

To prove ∠PRQ = ∠PSQ.

Construction Join OP and OQ.

Proof We know that the angle subtended by an arc at the centre is double the angle subtended by the arc at any point in the remaining part of the circle

We have, ∠POQ = 2∠PRQ and ∠POQ = 2∠PSQ

=> 2∠PRQ =2∠PSQ

=> ∠PRQ =∠PSQ