Angle in the same segment of a circle are equal.

Explanation

To prove: `/_PAQ=/_PBQ`
Proof: Chord `PQ` subtends `anglePOQ` at the center.
We know that the angle subtended by an arc of a circle at the center is double the angle subtended by it at any point on the remaining part of the circle.
`therefore/_PAQ=1/2/_POQ` ...(i)
`/_PBQ=1/2/_POQ` .....(ii)
From equation (i) and equation (ii), we get:
`/_PAQ=/_PBQ`
`therefore` Angle in the same segment of a circle are equal.
Hence Proved.