in lines AB and CD intersect at o. If Angle AOC + angle BOE = 70 and angle BOD = 40, find angle BOE and reflex angle COE
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For reflexing < COE :- 360° - 110°
< COE = 250°
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Question :-
In figure, lines AB and CD intersect at 0. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.
Answer :-
Since AB is a straight line,
∴ ∠AOC + ∠COE + ∠EOB = 180°
or (∠AOC + ∠BOE) + ∠COE = 180° or 70° + ∠COE = 180° [ ∵∠AOC + ∠BOE = 70° (Given)]
or ∠COE = 180° – 70° = 110°
∴ Reflex ∠COE = 360° – 110° = 250°
Also, AB and CD intersect at O.
∴∠COA = ∠BOD [Vertically opposite angles]
But ∠BOD = 40° [Given]
∴ ∠COA = 40°
Also, ∠AOC + ∠BOE = 70°
∴ 40° + ∠BOE = 70° or ∠BOE = 70° -40° = 30°
Thus, ∠BOE = 30° and reflex ∠COE = 250°.
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Similar questions
√BOD =40° (Given)
Find √BOE and reflex √COE
√AOC = √BOD =40° (V.O.A)
√AOC + √BOE =70°
40° + √BOE = 70°
√BOE = 70° - 40°
√BOE = 30°
Reflex √COE = √AOC + √COE + √BOE
√COE + 40° + 30° = 180° [ ∴ √AOB is a straight line ]
√COE + 70° = 180°
√COE = 180° - 70°
√COE = 110°
Reflex √COE = 360° - √COE = 360° - 110° = 250°
Ans. 30° , 250°
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