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.
• B.
• C.
• D.

Answer 1

The correct option is C

$\angle$ 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)$ = ${15}^{\circ }$.