Mathematics

In Fig., $POS$ is a line, find $x$.

20

SOLUTION
$POS$ is a line.
$\Rightarrow$  $\angle POQ+\angle QOS=180^o$               [ Linear pair ]
$\Rightarrow$  $\angle POQ+(\angle QOR+\angle ROS)=180^o$
$\Rightarrow$  $60^o+(4x+40^o)=180^o$
$\Rightarrow$  $100^o+4x=180^o$
$\Rightarrow$  $4x=80^o$

$\Rightarrow$  $x=\dfrac{80^o}{4}$

$\Rightarrow$  $x=20^o$

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