In Figure, POS is a line, find x. - Vidyadip

Question

In Figure, POS is a line, find x.

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Answer

Angles of a straight line,
$\angle \text{QOP}+\angle \text{QOR}+\angle \text{ROS}=108^\circ$
$\Rightarrow 60^\circ+4\text{x}+40^\circ=180^\circ$
$\Rightarrow 100^\circ+4\text{x}=180^\circ$
$\Rightarrow 4\text{x}=180^\circ-100^\circ$
$\Rightarrow4\text{x}=80^\circ$
$\Rightarrow \text{x}=\frac{80^\circ}{4}$
$\Rightarrow\text{x}=20^\circ$

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