In the figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70 and ∠BOD = 40, find ∠BOE and reflex ∠COE.

In given figure AB is a straight line and OC and OE meets at point O in AB.
∠AOC + ∠BOE + ∠COE = 180°
As given ∠AOC + ∠BOE = 70°
∴ 70° + ∠COE = 180°
⇒ ∠COE = 180° - 70° = 110°
Reflex ∠COE = 360° - ∠COE = 360° - 110° = 250°
∵ CD is a straight line and OE and OB stand on it
∠COE + ∠BOE + ∠BOD = 180°
110° + ∠BOE + 40° = 180°
∠BOE = 180° - 150°
⇒ ∠BOE = 30°