Regular Polygons

Where:
n = number of sides the polygon has

A regular polygon is a shape that has n amount of sides, all being equal length, symmetrical to one another, and sharing a common central point (n ≥ 3 and must be a whole number.) The number of a regular polygon's sides is always equal to the number of angles it contains. Also, because the sides of a regular polygon are all the same, all of its interior angles have the same value.

For much more information on regular polygons and how they're different from irregular polygons, refer to the help file for "Perimeter of a Regular Polygon".

This calculator gives the amount of sides, measure of each exterior angle, and measure of each interior angle of a regular polygon when one of these values is inputted.

Sum of All Angles
The sum of all the angles in a regular polygon is found by finding out how many triangles are in the polygon (found by subtracting 2 from the amount of the polygon's sides (n - 2) and multiplying this number by 180. We must multiply by 180 because the sum of all the angles in any triangle is 180 and, therefore, if we know the amount of triangles there are in a shape, we can multiply that by 180 to find the total sum of all the shape's angles.

Measure of Each Interior Angle
After we know the sum of all the polygon's angles, we can divide this by the number of sides the polygon has to get the measure of each individual angle. This works because (1) each angle inside of a regular polygon has the same value and (2) the number of a polygon's sides is equal to the number of angles it contains.

Measure of Each Exterior Angle
Once we know the measure of each interior angle, we can subtract this number by 180 to get the measure of each corresponding exterior angle.

To use this calculator, enter the number for the value that you have (either the number of sides the polygon has, the measure of each interior angle, or the measure of each exterior angle) and press the "Find" button next to it (in the same row.) If you press any other of the "Find" buttons, you will not get the right answers.

Works Cited
"Interior Angles." Coolmath4kids. 2005. Coolmath.com, Inc. 20 July 2006.
     <http://www.coolmath4kids.com/interior.html>.