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

Given that,

The lines and intersect at O.

∠AOC + ∠BOE = 70° ----(1)

∠BOD = 40° ----(2)

If the two lines intersect at a point then its vertically opposite angles are equal.

∴ ∠AOC = ∠BOD

Substitute (2) in (1)

⇒ 40° + ∠BOE = 70°

⇒∠BOE = 70°-40°

∴∠BOE = 30°

From the figure,AOB is a straight line and its angle is 180°

So, ∠AOC + ∠BOE + ∠COE = 180°

From equation (1)

⇒ 70° + ∠COE = 180°

⇒∠COE = 180°-70°

∴∠COE = 110°

Reflex ∠COE = 360° - 110° = 250°

∴∠BOE = 30° and Reflex ∠COE = 250°