Question

Lines AB and CD interesct at O. If $\angle$AOC = ${135}^{\circ }$, then $\frac{\angle BOC}{3}$ = .

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

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