In the Practice Run you learned that the interior angles sum of a convex polygon with n sides can be found using the expression (n − 2)180°. You can also use this expression to determine the individual interior angle measures in a regular polygon, a polygon with equal side lengths and angle measures.

The angles in a regular polygon are all equal, so dividing the interior angles sum by the number of angles in the polygon will give the measure of each angle. The measure of an individual interior angle in an n-sided polygon can be represented by .

Example 2

Each angle in a regular polygon measures 135°. How many sides does the polygon have?

This problem can be solved using .

The polygon has 8 sides. It is an octagon.