Mathematics

# In the figure, three coplanar lines $AB,CD$ and $EF$ intersect at a point $O$. Find the value of $x$. Hence, find $\angle AOD,\angle COE$ and $\angle AOE$

##### SOLUTION
From the figure we know that $\angle COE$ and $\angle EOD$ form a linear pair

$\angle COE+\angle EOD={ 180 }^{ o }$

It can also be written as

$\angle COE+\angle EOA+\angle AOD={ 180 }^{ o }$

By substituting values in the equation we get

$5x+\angle EOA+2x={ 180 }^{ o }$

From the figure we know that $\angle EOA$ and $\angle BOF$ are vertically opposite angles

$\angle EOA=\angle BOF$

so we get

$5x+\angle BOF+2x={180}^{o}$

$5x+3x+2x={ 180 }^{ o }$

$10x={ 180 }^{ o }$

$x=18$

By substituting the value of $x$

$\angle AOD=2{x}^{o}$

$\angle AOD=2(18)={36}^{o}$

$\angle EOA=\angle BOF=3{x}^{o}$

So we get

$\angle EOA=\angle BOF=3(!8)={54}^{o}$

$\angle COE=5{x}^{o}$

so we get

$\angle COE=5(18)={90}^{o}$

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Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
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