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 an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For a pentagon (\(n=5\)), the sum is \((5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Set up the equation

We know that \(x + 130+118 + 112+120=540\) (sum of interior angles of the pentagon).

Step3: Simplify the left - hand side of the equation

First, add the known angles: \(130 + 118+112 + 120=(130+120)+(118 + 112)=250+230 = 480\). So the equation becomes \(x+480 = 540\).

Step4: Solve for \(x\)

Subtract 480 from both sides of the equation: \(x=540 - 480\).

Answer:

\(x = 60\)