In the figure below, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70∘ and ∠BOD = 40∘, find (2 ∠BOE).
∠AOC + ∠BOE + ∠COE = 180∘ (linear pair of angle)
Given, ∠AOC + ∠BOE = 70∘
So, ∠COE = 180∘ – (∠AOC + ∠COE) = 180∘ – 70∘= 110∘
Again, ∠COE + ∠BOE + ∠BOD = 180∘ (linear pair of angle)
We know that, ∠COE = 110∘ and ∠BOD = 40∘
So, ∠BOE = 180∘ – ∠COE – ∠BOD = 180∘ – 110∘ – 40∘ = 30∘
(2 ∠BOE) = 60∘