Question

use the polygon sum to solve for x.

Explanation:

Step1: Calculate the sum of interior angles

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. Here \(n = 5\), so the sum is \((5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Set up the equation

We know that \(x + 75^{\circ}+75^{\circ}+105^{\circ}+115^{\circ}=540^{\circ}\).

Step3: Solve for \(x\)

First, add the known angles: \(75 + 75+105 + 115=370\). Then the equation becomes \(x+370^{\circ}=540^{\circ}\). Subtract \(370^{\circ}\) from both sides: \(x = 540^{\circ}-370^{\circ}\).

Answer:

\(x = 170^{\circ}\)