In the given figure, O is the centre of the circle and arc ABC subtends an angle of 130° at the centre. If AB is extended to P, find ∠PBC.
Reflex ∠AOC + ∠AOC = 360
⇒ Reflex ∠AOC + 130 + x = 360
⇒ Reflex ∠AOC = 360 − 130
⇒ Reflex ∠AOC = 230
We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by it on the remaining part of the circle.
Here, arc AC subtends reflex ∠AOC at the centre and ∠ABC at B on the circle.
∴ ∠AOC = 2∠ABC