Question

What is the measurement of angle POR

Answer 1

Let us observe the given figure,

When two lines intersect each other, the angles opposite to each other are Vertically Opposite Angles. Vertically opposite angles are always equal in measure.

As, we can observe that the given lines intersect each other, and they form vertically opposite angles as $\angle POR , \angle SOQ$ and  $\angle POS , \angle ROQ$

Therefore, $\angle POR = \angle SOQ$

Substituting the given measures of the angles, we get

$91-x^\circ = x+ 7^\circ$

$91-7 = x + x$

$84 = 2x$

$x = \frac{84}{2}$

So, x = $42^\circ$

Since, the measure of angle POR = $(91-x)^\circ$

= $(91-42)^\circ$

= $49^\circ$

Therefore, the measure of angle POR is 49 degrees.