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

When two straight lines intersect each other four angles are formed. The pair of angles which lie on the opposite sides of the point of intersection are called vertically opposite angles.
Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so alinear pair of angles must add up to 180 degrees

$\angle$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)