Answer
$x = 145$
Work Step by Step
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:
$120 + 116 + 129 + 130 + 135 + 125 + x = (7 - 2)180$
Evaluate what is in parentheses first, according to order of operations:
$120 + 116 + 129 + 130 + 135 + 125 + x = (5)180$
Multiply, according to order of operations:
$120 + 116 + 129 + 130 + 135 + 125 + x = 900$
Add the numbers on the left side of the equation:
$755 + x = 900$
Subtract $755$ from each side of the equation to solve for $x$:
$x = 145$
