Recall that we figured out in class how we can find the sum of the interior angles of any polygon (no matter what its shape) if we know the number of sides (n) using the formula:

180° × (n - 2)

A regular polygon with n sides has n equal angles. You can use the sum of interior angles formula to find the total of the interior angles, and then divide to find the size of one interior angle (because all of the angles are equal)

Example (video)

The sum of interior angles formula also works with an irregular polygon, so if you know all of the angles except one, you can subtract from the total angle sum to find the size of a missing angles

Example (video)

A regular polygon has a center. If you draw lines from the center out to the vertices of the polygon, the angles between those lines are called central angles. All of the central angles fill up the 360° around the center, so you can divide by the number of angles to find how big each central angle is of the regular polygon.

You can use the central angle of a polygon to figure out the size of an interior angle. To do this, you need to look at the triangles the central angles make inside the polygon. Those triangles are all isosceles triangles, and that means that the other two angles are the same size (have the same number of degrees). You can make an algebraic equation with those angles and the central angle that you know, and add up the angles, which is the 180° in a triangle. If you solve the equation, it will tell you how much half of an interior angle is, and you can use that to find out how big the interior angle is.

Example (video)

Another cool angle in a polygon is an exterior angle. It's kind of confusing to do exterior angles if there is a reflex angle in the polygon, so we're not going to worry about those polygons, and we'll just look at exterior angles in convex polygons. Watch this explanation of exterior angles, and what their sum is:

Exterior angle sum (video)

If the polygon is regular, then all of the interior angles are the same size as each other, and all of the exterior angles are the size of each other. We can divide to find the size of each of the exterior angles. The interior and exterior angles add up to 180°, so we can then subtract to find out the size of each of the interior angles.

Example (video)

Practice these ways of finding interior angles in this assignment.