In the given figure, is the center of the circle and arc subtends an angle of 130° at the center. If is extended to find

Question

In the given figure, is the center of the circle and arc subtends an angle of 130&#xB0; at the center. If is extended to find

Philoid · Accepted Answer

Reflex ∠AOC = 360° - ∠AOC

= 360° - 130°

= 230°

∴∠ABC = (1/2) ∠AOC

⇒ ∠ABC = (1/2) 230°

⇒ ∠ABC = 115°

Now,

∠ABC + ∠PBC = 180°[Because ABP is a straight line]

⇒ 115° + ∠PBC = 180°

⇒ ∠PBC = 65°