## Geometry: Common Core (15th Edition)

$x = 103$
To find the missing angle measures, we refer to the polygon angle-sum theorem, which states that the measure of all the interior angles of a $n-gon$ is $(n - 2)180$. Let's set up that equation using the interior angles we are given for this polygon: $100 + 117 + 105 + 115 + x = (5 - 2)180$ Evaluate what is in parentheses first, according to order of operations: $100 + 117 + 105 + 115 + x = (3)180$ Multiply, according to order of operations: $100 + 117 + 105 + 115 + x = 540$ Add the numbers on the left side of the equation: $437 + x = 540$ Subtract $437$ from each side of the equation to solve for $x$: $x = 103$