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

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Lines AB and CD intersect at O. 

∠AOC + ∠BOE = 70° (Given) …(1) 

∠BOD = 40° (Given) …(2) 

Since, ∠AOC = ∠BOD 

(Vertically opposite angles) 

Therefore, ∠AOC = 40° [From (2)] 

and 40° + ∠BOE = 70° [From (1)] 

⇒ ∠BOE = 70° – 40° = 30° 

Also, ∠AOC + ∠BOE + ∠COE = 180° 

(∵ AOB is a straight line) 

 70° + ∠COE = 180° [Form (1)] 

⇒ ∠COE = 180° – 70° = 110° 

Now, reflex ∠COE = 360° – 110° = 250° 

Hence, ∠BOE = 30° and reflex ∠COE = 250° Ans

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