Answer
$m \angle R = 135^{\circ}$
Work Step by Step
We first find the measures of the interior angles of this polygon. We find that by using the following formula:
sum of interior angles = $180(n - 2)$, where $n$ is the number of sides in the polygon.
Let's plug in the number of sides in this polygon:
sum of interior angles = $180(4 - 2)$
Evaluate what is in parentheses first:
sum of interior angles = $180(2)$
Multiply:
sum of interior angles = $360$
For $EZYD$, we now have three of the angles and the sum of the measures of the interior angles. We can use a formula to find the measure of the last angle, $\angle Z$:
$m \angle Z = 360 - (90 + 90 + 45)$
Evaluate what is in parentheses first:
$m \angle Z = 360 - (225)$
Subtract to solve for $\angle Z$:
$m \angle Z = 135^{\circ}$
In $TRAP$, $\angle R$ is congruent to $\angle Z$ in $EZYD$, so they have the same measures.
$m \angle R = 135^{\circ}$
