How to Find the Measure of an Interior Angle of a Regular Polygon

To find the measure of an interior angle of a regular polygon, you can use the formula:

Interior Angle = (n – 2) × 180° / n

Where n is the number of sides of the polygon. Here’s how it works:

1. First, determine the number of sides n in the polygon.
2. Subtract 2 from that number. This is because a polygon can be divided into (n – 2) triangles, and each triangle has a total angle measure of 180°.
3. Next, multiply the result by 180° to find the total measure of all the interior angles of the polygon.
4. Finally, divide that total by n to find the measure of a single interior angle.

For example, for a regular hexagon (which has 6 sides):

1. n = 6
2. (6 – 2) = 4
3. 4 × 180° = 720°
4. 720° / 6 = 120°

Therefore, each interior angle of a regular hexagon measures 120°.