## Geometry: Common Core (15th Edition)

$x = 159^{\circ}$
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. $m$ of the interior angles in a pentagon = $(5 - 2)180^{\circ}$ Evaluate what is in parentheses first, according to order of operations: $m$ of the interior angles in a pentagon = $(3)180^{\circ}$ Multiply to solve: $m$ of the interior angles in a pentagon = $540^{\circ}$ We are given the measures of four of the five angles in this pentagon. If we add these interior angles together and subtract them from $540^{\circ}$, then we will get the measure of the fifth angle, $x$: $x = 540^{\circ} - (90 + 83 + 89 + 119)^{\circ}$ Evaluate what is in parentheses first, according to order of operations: $x = 540^{\circ} - (381^{\circ})$ Subtract to solve: $x = 159^{\circ}$