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

Question

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

Philoid · Accepted Answer

Given: ∠AOC = 130°

Here,

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

(Exterior ∠AOC) = 360° – 130°

(Exterior ∠AOC) = 230°

We know that,

(Exterior ∠AOC) = 2 × ∠ABC

230° = 2 × ∠ABC

∠ABC = = 115°

∴ ∠ABC = 115°