Question

In figure, $\angle POR:\angle ROQ=5:7$. The value of $\angle POR$ is:

• A. ${60}^o$
• B. ${65}^o$
• C. ${75}^o$
• D. ${90}^o$

Answer 1

The correct option is C ${75}^o$

$\angle POR+\angle ROQ$ = ${180}^o$ ...(1) [ Linear Pair]
But $\frac{\angle POR}{\angle ROQ}$ = $\frac{5}{7}$ [Given]
$\Rightarrow$ $\angle$ROQ = $\frac{7}{5}\angle POR$ ... (2)

From (1) and (2), we have
$\angle POR+\frac{7}{5}\angle POR$ = 180${}^o$
$\Rightarrow \frac{12}{5}\angle POR$ = 180${}^o$
$\Rightarrow \angle POR$ = $\frac{{180}^o\times 5}{12}$
$\Rightarrow \angle POR$ = 75${}^o$

Now, $\angle$SOQ = $\angle$POR = 75${}^o$ (Vertically opposite angles)