Question

Lines PQ and RS intersect at O. If $\angle POR$ is three times $\angle ROQ$, then $\angle SOQ$ is

• A. ${120}^{\circ }$
• B. ${150}^{\circ }$
• C. ${135}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is C ${135}^{\circ }$

$\angle POR=3\angle ROQ$ (Given)
$\angle POR+\angle ROQ={180}^{\circ }$ (Linear pair)
$\Rightarrow 3\angle ROQ+\angle ROQ={180}^{\circ }$
$\Rightarrow 4\angle ROQ={180}^{\circ }$
$\Rightarrow \angle ROQ=\frac{{180}^{\circ }}{4}={45}^{\circ }$
Now $\angle SOQ=\angle POR$
$=3\angle ROQ$ (Ver. opp. $\angle s$)
$=3\times {45}^{\circ }={135}^{\circ }$