Question

3(Arc BC) = Arc AB, ∠AOB = 120°, ∠BOC = 

Options

• 60°

• 50°

• 45°

• 40°

Answer 1

40°

Explanation:

From the given condition, 3(Arc BC) = Arc AB and ∠AOB = 120°:

1. Relationship between arcs and angles at the centre:

The angle subtended by an arc at the centre equals the measure of that arc.

So, Arc AB = 120°

And `Arc  BC = ("Arc" AB)/3`

= `120^circ/3`

= 40°

2. Finding ∠BOC:

Arc BC subtends ∠BOC at the centre, so:

∠BOC = Arc BC = 40°