In Fig. 8.62, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40° find ∠BOE and reflex ∠COE.

Question

In Fig. 8.62, lines AB and CD intersect at O . If &#x2220; AOC + &#x2220; BOE = 70&#xB0; and &#x2220; BOD = 40&#xB0; find &#x2220; BOE and reflex &#x2220; COE.

Philoid · Accepted Answer

Given that,

∠AOC + ∠BOE = 70^o

And,

∠BOD = 40^o

∠BOF =?

∠BOD = ∠AOC = 40^o (Vertically opposite angle)

Given,

∠AOC + ∠BOE = 70^o

40^o + ∠BOE = 70^o

∠BOE = 70^o – 40^o

= 30^o

∠AOC and ∠BOC are linear pair angle

∠AOC + ∠COE + ∠BOE = 180^o

∠COE = 180^o – 30^o – 40^o

= 110^o

Therefore,

∠COE = 360^o – 110^o

= 250^o

In Fig. 8.62, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40° find ∠BOE and reflex ∠COE.