Question

In the given figure, AB is the diameter of the circle with centre O.

If ∠ADC = 32°, find angle BOC.

Answer 1

Arc AC subtends ∠AOC at the centre and ∠ADC at the remaining part of the circle

∴ ∠AOC = 2∠ADC

`=>` ∠AOC = 2 × 32° = 64°

Since ∠AOC and ∠BOC are linear pair, we have

∠AOC + ∠BOC = 180°

`=>` 64° + ∠BOC = 180°

`=>` ∠BOC = 180°

`=>` ∠BOC = 180° – 64°

`=>` ∠BOC = 116°