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

To solve this, we will just employ basic arithmetic in geometry.

x = 45°

We are given a polygon with 5 sides and also given each angle. However, we are told that their sum is 540° and so we will add all the five angles and equate to 540°.

Thus;

4x° + 4x° + (5x + 2)° + 96° + (5x - 8)° = 540

Opening the brackets and simplifying, we have;

18x + 90 = 540

Subtracting 90 from both sides and we have;

18x = 540 - 90

18x = 450

x = 450/18

x = 45°

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Let's set the measure of each angle equal to 540 degrees.

4x + 4x + 5x + 2 + 96 + 5x - 8 = 540

Combine like terms.

18x + 90 = 540

Subtract 90 from both sides.

18x = 450

Divide both sides by 18

x = 25