## Geometry: Common Core (15th Edition)

$z = 69$
First, let's find what the measure of all the interior angles is for this polygon. According to Polygon Angle-Sum Theorem, the sum of all the measures of the interior angles of a polygon is $(n - 2)180$, where $n$ is the number of sides of the polygon. We have a polygon that has $4$ sides. Let's find out the sum of the measures of all the interior angles in this polygon by using this formula: $m$ of the interior angles in a quadrilateral = $(4 - 2)180$ Evaluate what is in parentheses first, according to order of operations: $m$ of the interior angles in a quadrilateral = $(2)180$ Multiply to solve: $m$ of the interior angles in a quadrilateral = $360^{\circ}$ We are given the measures of three of the four angles in this quadrilateral. If we add these interior angles together and subtract them from $360$, then we will get the measure of the fourth angle, $z$: $z = 360 - (90 + 122 + 79)$ Evaluate what is in parentheses first, according to order of operations: $z = 360 - 291$ Subtract to solve: $z = 69$