Question

In the given figure, O is the centre of the circle. Determine

1. ∠ABC
2. Reflex ∠AOС

Answer 1

Given:

At point D, the exterior angle formed by chord DC is 68°.

This exterior angle equals the opposite interior inscribed angle, which is ∠ABC.

i. ∠ABC

Exterior angle theorem for a circle:

Exterior angle at D = Opposite interior inscribed angle

So, ∠ABC = 68°

ii. Reflex ∠AOC

∠ABC and the central angle AOC both subtend the same arc AC.

∠AOC = 2 × ∠ABC

∠AOC = 2 × 68° = 136°

But we need the reflex angle, so:

Reflex ∠AOC = 360° − 136° = 224°