In the given figure, O is the centre of the circle and arc ABC subtends an angle of 130° at the centre.

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

$\Rightarrow \angle A B C=\frac{230^{\circ}}{2}=115^{\circ}$        ...(1)

Since ABP is a straight line, ∠ABC + ∠PBC = 180∘
⇒ ∠PBC = 180∘ − 115∘
⇒ ∠PBC = 65∘            ...(2)

Hence, ∠PBC = 65∘.