Question

In the figure given below, a ray OC extends from a point O on a straight line AB, If ∠AOC = 135°, then $\frac{\angle BOC}{3}$ is equal to _____.

• A. ${20}^{\circ }$
• B. ${15}^{\circ }$
• C. ${45}^{\circ }$
• D. ${65}^{\circ }$

Answer 1

The correct option is B ${15}^{\circ }$

∠AOC + ∠BOC = 180°
[Linear pair of angles]

Given that,
∠AOC = 135°
135° + ∠BOC = 180°
∠BOC = 180° - 135°
∠BOC = 45°
$\frac{\angle BOC}{3}$ = $\frac{{45}^{\circ }}{3}$= ${15}^{\circ }$