## Geometry: Common Core (15th Edition)

$m \angle R = 135^{\circ}$
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. $m \angle R = 135^{\circ}$