In the given figure, O is the centre of a circle and ∠AOB = 140°. Then, ∠ACB = ?

Question

In the given figure, O is the centre of a circle and ∠ AOB = 140°. Then, ∠ ACB = ?

Philoid · Accepted Answer

Given: ∠AOB = 140°

Here,

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

(Exterior ∠AOB) = 360° – 140°

(Exterior ∠AOB) = 220°

We know that,

(Exterior ∠AOB) = 2 × ∠ACB

220° = 2 × ∠ACB

∠ACB = = 110°

∴ ∠ACB = 110°