Question

In the given figure what is the measure of angleABC ?​

Answer 1

Answer: ∠ABC = 40°

Explanation:

∠AOC = 80°                                    (Given)

∴ ∠ABC = $\frac{1}{2}$ × ∠AOC

Theorem:

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Here, the arc AC subtends ∠AOC at the centre, O and ∠ABC at point B on the remaining part of the circle.

⇒ ∠ABC = $\frac{1}{2}$ × 80°

⇒ ∠ABC = 40°

Hence, proved.

Hope you got that.

Thank You.