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Question
In the given figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.
Solution
AB is a straight line, and rays OC and OE stand on it.
∴ ∠AOC + ∠COE + ∠BOE = 180°
⇒ (∠AOC + ∠BOE) + ∠COE = 180°
⇒ 70° + ∠COE = 180°
⇒ ∠COE = 180° − 70° = 110°
Reflex ∠COE = 360° − 110° = 250°
The CD is a straight line, and rays OE and OB stand on it.
∴ ∠COE + ∠BOE + ∠BOD = 180°
⇒ 110° + ∠BOE + 40° = 180°
⇒ ∠BOE = 180° − 150° = 30°
Thus, ∠BOE = 30° and reflex ∠COE = 250°
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