Question

In the given figure, lines RS and PQ intersect at point O. If ∠POR : ∠ROQ = 11 : 13, ∠SOQ = _____ .

• A. $82.5^o$
• B. $97.5^o$
• C. ${95}^o$
• D. ${65}^o$

Answer 1

The correct option is A $82.5^o$

$\angle POR+\angle ROQ={180}^o---\left(1\right)\left[linearpair\right]$
Given that $\angle POR:\angle ROQ=11:13$, let $\angle POR=11x$ and $\angle ROQ=13x$.
Then, eq. $\left(1\right)$ becomes $11x+13x={180}^o\Rightarrow 24x={180}^o\Rightarrow x=7.5^o$

Thus, $\angle POR=11x=82.5^o$ and $\angle ROQ=13x=97.5^o$.
Now, $\angle POR$ and $\angle SOQ$ are equal as they are vertically opposite angles.
Hence, $\angle SOQ=\angle POR=82.5^o$.