Question

In the figure below, a ray OC extends from a point O on a straight line AB. If $\angle$AOC = ${135}^{\circ }$, then $\left(\frac{\angle BOC}{3}\right)$ is equal to :

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

Answer 1

The correct option is C

${15}^{\circ }$

$\angle$ AOC + $\angle$ BOC = ${180}^{\circ }$ $\because$ they form a linear pair.

Given that, $\angle$ AOC = ${135}^{\circ }$

$\Rightarrow$${135}^{\circ }$ + $\angle$ BOC = ${180}^{\circ }$

$\Rightarrow$$\angle$ BOC = ${180}^{\circ }$ - ${135}^{\circ }$

$\Rightarrow$$\angle$ BOC = ${45}^{\circ }$
$\Rightarrow$$\left(\frac{\angle BOC}{3}\right)$ = ${15}^{\circ }$.