Question

Given, $\angle POR=3x$ and $\angle QOR=2x+{10}^{\circ }$, find the values of $x$ for which $POQ$ will be a line.

Answer 1

Since, $POQ$ is a line

$\Rightarrow \angle QOR$ and $\angle POR$ are forming linear pair

$\Rightarrow \angle QOR+\angle POR={180}^{\circ }$

$\Rightarrow 3x+2x+{10}^{\circ }={180}^{\circ }$

$\Rightarrow 5x={180}^{\circ }-{10}^{\circ }$

$\Rightarrow x=\frac{{170}^{\circ }}{5}$

$\Rightarrow x={34}^{\circ }$

Hence, the value of $x$ is ${34}^{\circ }.$