In the given figure, O is the centre of a circle and ∠AOB = 130°. Then, ∠ACB = ?

Question

In the given figure, O is the centre of a circle and ∠ AOB = 130°. Then, ∠ ACB = ?

Philoid · Accepted Answer

Given: ∠AOB = 130°

Here,

(Exterior ∠AOB) = 360° – (interior ∠AOB)

(Exterior ∠AOB) = 360° – 130°

(Exterior ∠AOB) = 230°

We know that,

(Exterior ∠AOB) = 2 × ∠ACB

230° = 2 × ∠ACB

∠ACB = = 115°

∴ ∠ACB = 115°