Question

In the figure given below, lines AB and CD interest at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, then the value of 2∠BOE is:

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

Answer 1

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

∠AOC + ∠BOE + ∠COE = 180°
[Linear pair of angles]

Given that ∠AOC + ∠BOE = 70°
So, ∠COE = 180° - (∠AOC + ∠COE)
= 180° - 70° = 110°
Again, ∠COE + ∠BOE + ∠BOD = 180° [Linear pair of angles]
We know that , ∠COE = 110° and
∠BOD = 40°
So, ∠BOE = 180° - ∠COE - ∠BOD
∠BOE = 180° - 110° - 40°
= 30°
Hence, 2∠BOE = 60°