Mathematics

# In the figure, $AOB$ is a straight line. Find the value of $x$. Here, find $\angle AOC,\angle COD$ and $\angle BOD$

##### SOLUTION
From the figure, we know that $\angle BOD$ and $\angle AOD$ are linear pair of angles

So we get

$\angle BOD+\angle AOD={180}^{o}$

It can also be written as

$\angle BOD+\angle COD+\angle COA={180}^{o}$

By substituting the values

${ x }^{ o }+{ \left( 2x-19 \right) }^{ o }+{ \left( 3x+7 \right) }^{ o }={ 180 }^{ o }$

$\Rightarrow x+2x-{ 19 }^{ o } +3x+{ 7 }^{ o }={ 180 }^{ o }$

$\Rightarrow 6x-{ 12 }^{ o }={ 180 }^{ o }$

$\Rightarrow 6x={ 192 }^{ o }\Rightarrow x={ 32 }^{ o }$

By substituting the value of $x$ we get

$\angle AOC={ \left( 3x+7 \right) }^{ o }=3({32}^{o})+{7}^{o}={103}^{o}$

$\angle COD={ \left( 2x-19 \right) }^{ o }=2({32}^{o})-{19}^{o}={45}^{o}$

$\angle BOD={x}^{o}={32}^{o}$

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