Question

In the figure below, lines AB and CD intersect at O. If $\angle$AOC + $\angle$BOE = ${70}^{\circ }$ and $\angle$BOD = ${40}^{\circ }$, find (2$\angle$BOE).

• A. ${50}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is C

${60}^{\circ }$

$\angle AOC+\angle BOE+\angle COE={180}^{\circ }$ (AOB is a straight line)

Given, $\angle AOC+\angle BOE={70}^{\circ }$

So, $\angle COE={180}^{\circ }–(\angle AOC+\angle COE)$

$\Rightarrow {180}^{\circ }–{70}^{\circ }={110}^{\circ }$

Again, $\angle COE+\angle BOE+\angle BOD={180}^{\circ }$ (COD is a straight line)

We know that, $\angle COE={110}^{\circ }$ and $\angle BOD={40}^{\circ }$

So, $\angle BOE={180}^{\circ }–\angle COE-\angle BOD$

$\Rightarrow \angle BOE={180}^{\circ }–{110}^{\circ }-{40}^{\circ }={30}^{\circ }\Rightarrow 2\angle BOE={60}^{\circ }$