Question

In the figure below, lines RS and PQ intersect each other at point O. If the ratio of $\angle POR:\angle ROQ=11:13$ , find $\angle SOQ$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\angle$POR + $\angle$ROQ = ${180}^{\circ }$ (linear pair of angles)

but, $\angle$POR : $\angle$ROQ = 11:13 (given)

$\angle$POR = $\frac{11}{24}$ $\times$ ${180}^{\circ }$ = $(\frac{165}{2}{)}^{\circ }$

Similarly, $\angle$ROQ = $\frac{13}{24}$ $\times$ ${180}^{\circ }$ = $(\frac{195}{2}{)}^{\circ }$

Now, $\angle$POS = $\angle$ROQ = $(\frac{195}{2}{)}^{\circ }$ (vertically opposite angle)

And, $\angle$SOQ = $\angle$POR= $(\frac{165}{2}{)}^{\circ }$ (vertically opposite angle)