Q17 of 50 Page 6

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

It is given: ∠AOC + ∠BOE = 70o


And, ∠BOD = 40o


Now, according to the question,


∠AOC + ∠BOE + ∠COE = 180o (Sum of linear pair is always 180o )


⇒ 70o + ∠COE = 180o


⇒ ∠COE = 110o ...........(1)


And,


∠COE + ∠BOD + ∠BOE = 180o(Sum of linear pair is always 180o )


putting the value of ∠COE, we get,


110o + 40o + ∠BOE = 180o


150o + ∠BOE = 180o


∴ ∠BOE = 30o


Now, reflex ∠COE = 360o - ∠COE


⇒ reflex ∠COE = 360o - 110o


∴ reflex ∠COE = 250o


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