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
To find BOE
Here, BOD and AOC an vertically opposite angles
BOD = AOC = 40
Given, ∠AOC + ∠BOE = 70°,
⟹ 40 + BOF = 70
⟹ BOF = 70 - 40
⟹ BOE = 30
AOC and BOC are lines pair of angles
⟹ AOC + COF + BOE = 180
⟹ COE = 180 - 30 - 40
⟹ COE = 110
Hence, Reflex COE = 360 - 110 - 250.