As shown in above figure AB and CD are two parallel lines and a line XY passes through them and intersects AB at P & CD at Q. If ∠DQX=x∘ then ∠APY= ___.
∵ ∠BPY and ∠DQX are supplementary angles so ∠BPY=180∘−x∘
∠BPY and ∠APY are supplementary angles.
⇒ 180∘−x∘+∠APY=180∘ ⇒ ∠APY=x∘
Also, ∠APY=∠DQX=x∘ (Since they are alternate interior angles)
In the figure below, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70∘ and ∠BOD = 40∘, find (3∠BOE).