Question

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

Answer 1

∠AOC = ∠BOD = 40° 

∠BOD = 40° (Date) 

∠AOC = ∠BOD = 40° because vertifically opposite angles.

∴ ∠AOC + ∠BOE = 70° 

40° + ∠BOE = 70°

∴ ∠BOE = 70° – 40° = 30°, and 

∠AOD = 180° – ∠BOD = 180° – 40° = 140° 

Reflex angle COE = ∠COA + ∠AOD + ∠BOD + ∠BOE 

= 40° + 140° + 40° + 30° 

∴ Reflex angle, ∠COE = 250°.