Question

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

Answer 1

Given that

`∠`AOC + `∠`BOE = 70° and `∠`BOD = 40°

`∠`BOE = ?

Here,  `∠`BOD and  `∠`AOC are vertically opposite angles

`∠`BOD = `∠`AOC = 40°

Given `∠`AOC + `∠`BOE = 70°

40° + `∠`BOF = 70°

`∠`BOF = 70° - 40°

`∠`BOE = 30°

`∠`AOC and `∠`BOC are linear pair of angles

⇒`∠`AOC + `∠`COF + `∠`BOE = 180°

⇒ `∠`COE = 180° - 30° - 40°

⇒ `∠`COE = 110°

∴Reflex `∠`COE = 360° -110° = 250°.