MCQ
Lines $PQ$ and $RS$ intersect at $O.$ If $\angle\text{POR}$ is three times $\angle\text{ROQ}$, then $\angle\text{SOQ}$ is:
- A$120^\circ$
- B$150^\circ$
- ✓$135^\circ$
- D$45^\circ$
$\angle\text{POR}=3\angle\text{ROQ}$ (Given)
$\angle\text{POR}+\angle\text{ROQ}=180^\circ$
$\Rightarrow3\angle\text{ROQ}+\angle\text{ROQ}=180^\circ$
$\Rightarrow4\angle\text{ROQ}=180^\circ$
$\Rightarrow\text{ROQ}=\frac{180^\circ}{4}=45^\circ$
Now, $\angle\text{SOQ}=\angle\text{POR}$
$=3\angle\text{ROQ }(\text{Ver. opp.}{\angle\text{S}})$
$=3\times45^\circ=135^\circ$
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