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

Given :

∠BOD = 40°

From figure,

⇒ ∠AOC = ∠BOD (Vertically opposite angles are equal)

⇒ ∠AOC = 40°

Given,

⇒ ∠AOC + ∠BOE = 70°

⇒ ∠BOE = 70° - ∠AOC = 70° - 40° = 30°.

Since, AB is a straight line.

From figure :

⇒ ∠AOC + ∠COE + ∠BOE = 180° [Linear pairs]

⇒ ∠COE + (∠AOC + ∠BOE) = 180°

⇒ ∠COE + (40° + 30°) = 180°

⇒ ∠COE + 70° = 180°

⇒ ∠COE = 180° - 70° = 110°.

⇒ Reflex ∠COE = 360° - ∠COE = 360° - 110° = 250°.

Hence, ∠BOE = 30° and Reflex ∠COE = 250°.