Mathematics

In the figure, what value of $$x$$ will make $$AOB$$, a straight line?


SOLUTION
We know that 

$$AOB$$ will be straight line only if the adjacent angles form a linear pair

$$\angle BOC+\angle AOC={ 180 }^{ o }$$

$${ x }+{ \left( 4x-36 \right)  }^{ o }+{ \left( 3x+20 \right)  }^{ o }={ 180 }^{ o }$$

$$\Rightarrow 4x-{ 36 }^{ o }+3x+{ 20 }^{ o }={ 180 }^{ o }$$

$$\Rightarrow 7x={ 180 }^{ o }-{ 20 }^{ o }+{ 36 }^{ o }$$

$$\Rightarrow 7x={ 196 }^{ o }\quad$$

$$ \Rightarrow x={ 28 }^{ o }$$

Therefore the value of $$x$$ is $$28$$
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