Question

use the polygon sum to solve for x.

Explanation:

Step1: Calculate the sum of interior angles

For a pentagon ($n = 5$), the sum of interior angles is $(n - 2)\times180^{\circ}=(5 - 2)\times180^{\circ}=540^{\circ}$.

Step2: Set up the equation

$x+75^{\circ}+105^{\circ}+75^{\circ}+115^{\circ}=540^{\circ}$.

Step3: Solve for $x$

$x+475^{\circ}=540^{\circ}$, so $x = 540^{\circ}-475^{\circ}=65^{\circ}$.

Answer:

$65^{\circ}$