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. ${60}^{\circ }$
• C. ${80}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is B

${60}^{\circ }$

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

Given $\angle$BOD = ${40}^{\circ }$

$\Rightarrow$ $\angle$AOC = ${40}^{\circ }$ (Vertically opposite angles)

$\Rightarrow$ $\angle$BOE = ${70}^{\circ }$ - $\angle$AOC

= ${70}^{\circ }$ - ${40}^{\circ }$

= ${30}^{\circ }$
Therefore, 2 $\angle$BOE = ${60}^{\circ }$