Question

1. what is m∠r?

Explanation:

Step1: Recall sum of angles in a quadrilateral

The sum of interior - angles of a quadrilateral is $360^{\circ}$.

Step2: Set up the equation

Let $m\angle R=x$. We know the other three angles are $111^{\circ}$, $62^{\circ}$, and assume the fourth angle is $y$. So $x + 111^{\circ}+62^{\circ}+y=360^{\circ}$.
However, if we assume the two quadrilaterals are congruent (since side - lengths match and some angle - measures match), we can also use the fact that corresponding angles of congruent figures are equal. In the second quadrilateral, we have angles $80^{\circ}$, $107^{\circ}$, $62^{\circ}$.
We calculate the fourth angle of the second quadrilateral: $360-(80 + 107+62)=360 - 249=111^{\circ}$.
Since the two quadrilaterals seem to be congruent (by SSS - like and angle - angle correspondences), $m\angle R = 107^{\circ}$.

Answer:

$107^{\circ}$