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. ${90}^{\circ }$

Answer 1

The correct option is C ${60}^{\circ }$

$\angle AOC+\angle BOE+\angle COE={180}^{\circ }$ (Linear pair of angles).
Given, $\angle AOC+\angle BOE={70}^{\circ }$
So, $\angle COE=180-(\angle AOC+\angle COE)$
$\Rightarrow {180}^{\circ }-{70}^{\circ }={110}^{\circ }$
Again, $\angle COE+\angle BOE+\angle BOD={180}^{\circ }$ (Linear pair of angles)
We know that, $\angle COE={110}^{\circ }$ and $\angle BOD={40}^{\circ }$
So, $\angle BOE={180}^{\circ }-\angle COE-\angle BOD$
$\Rightarrow {180}^{\circ }-{110}^{\circ }-{40}^{\circ }={30}^{\circ }$
Hence, $2\angle BOE={60}^{\circ }$