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 \(S=(5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Set up the equation

We know that \(x+130 + 120+112 + 118=540\).

Step3: Simplify the left - hand side of the equation

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

Step4: Solve for \(x\)

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

Answer:

\(x = 60\)