In Fig., lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and

1.	In Fig., lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40° find ∠BOE and reflex ∠COE.
Answer» Given that, ∠AOC + ∠BOE = 70° And, ∠BOD = 40° ∠BOF = ? ∠BOD = ∠AOC = 40°(Vertically opposite angle) Given, ∠AOC + ∠BOE = 70° 40° + ∠BOE = 70° ∠BOE = 70° – 40° = 30° ∠AOC and ∠BOC are linear pair angle ∠AOC + ∠COE + ∠BOE = 180° ∠COE = 180° – 30° – 40° = 110° Therefore, ∠COE = 360° – 110° = 250°

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

Answer»

Given that,

∠AOC + ∠BOE = 70°

And,

∠BOD = 40°

∠BOF = ?

∠BOD = ∠AOC = 40°(Vertically opposite angle)

Given,

∠AOC + ∠BOE = 70°

40° + ∠BOE = 70°

∠BOE = 70° – 40°

= 30°

∠AOC and ∠BOC are linear pair angle

∠AOC + ∠COE + ∠BOE = 180°

∠COE = 180° – 30° – 40°

= 110°

Therefore,

∠COE = 360° – 110°

= 250°