in the given figure lines AB and CD intersect at O.if angle AOC+ angle BOE=70 and angle DOB=40,find the reflex angle EOC
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Given:∠BOD=40 ∘
Since AB and CD intersects, ∠AOC=∠BOD(vertically opposite angles)
∠AOC=40 ∘
Also,∠AOC+∠BOE=70 ∘
⇒∠BOE=70 ∘
−∠AOC=70 ∘
−40 ∘
=30 ∘
We need to find reflex∠COE
Reflex∠COE=360 ∘
−∠COE
Now, ∠AOC+∠COE+∠BOE=180 ∘
⇒∠COE+(∠AOC+∠BOE)=180 ∘
⇒∠COE+(40 ∘
+30 ∘
)=180 ∘
⇒∠COE=180 ∘
−70 ∘
=110 ∘
Reflex∠COE=360 ∘
−110 ∘
=250 ∘
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