Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

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

Given, ∠AOC + ∠BOE = ${70}^{\circ }$

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

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

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

So,∠BOE = ${180}^{\circ }$ –∠COE - ∠BOD => ${180}^{\circ }$ – ${110}^{\circ }$ - ${40}^{\circ }$ = ${30}^{\circ }$
(2∠BOE) = ${60}^{\circ }$