In the figure below, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70∘ and ∠BOD = 40∘, find (2∠BOE).
60∘
∠AOC + ∠BOE + ∠COE = 180∘ (Linear pair of angles).Given,∠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 ⇒ 180∘ – 110∘ - 40∘ = 30∘.
Hence, 2 ∠BOE = 60∘.