Question

Line AB and Cd intersect at O . If angle AOC + BOE =70° and angle BOD = 40° find angle BOE and reflex of angle COE

Answer 1

Answer:

Given:∠BOD=40

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Since AB and CD intersects, ∠AOC=∠BOD(vertically opposite angles)

∠AOC=40

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Also,∠AOC+∠BOE=70

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⇒∠BOE=70

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−∠AOC=70

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−40

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=30

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We need to find reflex∠COE

Reflex∠COE=360

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−∠COE

Now, ∠AOC+∠COE+∠BOE=180

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⇒∠COE+(∠AOC+∠BOE)=180

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⇒∠COE+(40

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+30

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)=180

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⇒∠COE=180

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−70

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=110

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Reflex∠COE=360

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−110

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=250

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Answer 2

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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