Question

In the adjoining figure,three lines AB,CD and EF intersect at a point O.Find the value of x.Hence,find<AOD,<COE and <AOE.​

Answer 1

Answer:

From the figure we know that ∠COE and ∠EOD form a linear pair

∠COE + ∠EOD = 180°

It can also be written as

∠COE + ∠EOA + ∠AOD = 180°

By substituting values in the above equation we get

5x + ∠EOA + 2x = 180°

From the figure we know that ∠EOA and ∠BOF are vertically opposite angles

∠EOA = ∠BOF

So we get

5x + ∠BOF + 2x = 180°

5x + 3x + 2x = 180°

On further calculation

10x = 180°

By division

x = 180/10 = 18

By substituting the value of x

∠AOD = 2x°

So we get

∠AOD = 2 (18)° = 36°

∠EOA = ∠BOF = 3x°

So we get

∠EOA = ∠BOF = 3 (18)° = 54°

∠COE = 5x°

So we get

∠COE = 5 (18)° = 90°

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