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 $\left(2\angle BOE\right)$.

• A. ${30}^{\circ }$
• B. ${90}^{\circ }$
• C. ${50}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is D

${60}^{\circ }$

$\angle AOC+\angle BOE+\angle COE={180}^{\circ }$ (linear pair of angle)

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

So, $\angle COE={180}^{\circ }–(\angle AOC+\angle COE)\Rightarrow {180}^{\circ }–{70}^{\circ }={110}^{\circ }$

Again, $\angle COE+\angle BOE+\angle BOD={180}^{\circ }$ (linear pair of angle)

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

So, $\angle BOE={180}^{\circ }–\angle COE-\angle BOD\Rightarrow {180}^{\circ }–{110}^{\circ }-{40}^{\circ }={30}^{\circ }$
$\left(2\angle BOE\right)={60}^{\circ }$