Question

In the given figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = ${70}^o$ and ∠BOD = ${40}^o$, the value of 2(∠BOE) is ____.

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

Answer 1

The correct option is C ${60}^o$

In the given figure, $\angle AOC=\angle BOD={40}^o\left[verticallyoppositeangles\right]$
Given that $\angle AOC+\angle BOE={70}^o,$ we get ${40}^o+\angle BOE={70}^o$$\Rightarrow \angle BOE={30}^o$
Thus, $2(\angle BOE)={60}^o$.