Question

the sum of the angle measures is 540°. write and solve an equation to find the value of x.

Explanation:

Step1: Set up the equation

The sum of the angle - measures of the polygon is given as \(540^{\circ}\), and the angle - measures are \(90^{\circ}, 90^{\circ}, 120^{\circ}, 120^{\circ}, x\). So the equation is \(90 + 90+120 + 120+x=540\).

Step2: Simplify the left - hand side

First, add the known angles: \(90 + 90+120 + 120=420\). The equation becomes \(420 + x=540\).

Step3: Solve for \(x\)

Subtract 420 from both sides of the equation: \(x=540 - 420\).

Answer:

\(x = 120\)