Question

use the polygon sum to solve for x.

Explanation:

Step1: Recall the polygon sum formula

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 the angles of the pentagon are \(90^{\circ}\), \(120^{\circ}\), \(112^{\circ}\), \(118^{\circ}\), and \(x^{\circ}\). So, \(90 + 120+112 + 118+x=540\).

Step3: Simplify the left - hand side of the equation

\(90+120 = 210\), \(210+112=322\), \(322 + 118=440\). The equation becomes \(440+x=540\).

Step4: Solve for \(x\)

Subtract 440 from both sides: \(x=540 - 440\).

Answer:

\(x = 100\)