Question

6. In the adjacent diagram two lines AB and CD intersect at O. If the ratio of the angles ∠AOC, ∠BOE and ∠AOD are 1 ∶ 2 ∶ 5, then find the measure of reflex ∠COE.

Answer 1

Given : Two lines AB and CD intersect at O. If the ratio of the angles ∠AOC, ∠BOE and ∠AOD are 1 ∶ 2 ∶ 5,  

To find : ∠COE.

Solution:

∠AOC, ∠BOE and ∠AOD are 1 ∶ 2 ∶ 5

∠AOC  =  A

∠BOE  = 2A

∠AOD = 5A

∠AOC +  ∠AOD  = 180°

=> A + 5A = 180°

=> 6A = 180°

=> A = 30°

∠AOC  =  30°

∠BOE  = 60°

∠AOD = 150°

∠AOC + ∠COE  + ∠BOE   = 180°

=> 30° + ∠COE  + 60°  = 180°

=> ∠COE = 90°

Reflex of  ∠COE = 360° - 90°  = 270°

∠COE = 90°  

Reflex of  ∠COE =  270°

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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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