Answer
$z = 69$
Work Step by Step
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:
$z = 69$
