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Question
In below figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD =
40°, find ∠BOE and reflex ∠COE.
Solution
Given that
`∠`AOC + `∠`BOE = 70° and `∠`BOD = 40°
`∠`BOE = ?
Here, `∠`BOD and `∠`AOC are vertically opposite angles
`∠`BOD = `∠`AOC = 40°
Given `∠`AOC + `∠`BOE = 70°
40° + `∠`BOF = 70°
`∠`BOF = 70° - 40°
`∠`BOE = 30°
`∠`AOC and `∠`BOC are linear pair of angles
⇒`∠`AOC + `∠`COF + `∠`BOE = 180°
⇒ `∠`COE = 180° - 30° - 40°
⇒ `∠`COE = 110°
∴Reflex `∠`COE = 360° -110° = 250°.
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