The word polygon is a collective term for all triangles, quadrilaterals, pentagons, and so on.
Theory
A figure is regular if all its sides have the same length, and all its angles are the same size.
Examples of regular polygons are:
A regular triangle—an equilateral triangle.
A regular quadrilateral—a square.
Formula
The central angle of a regular polygon is the angle between two lines that go from the center of the polygon to two neighboring vertices.
The central angle of a regular polygon with sides can be calculated by using the formula
Here’s a regular hexagon:
Example 1
You have a regular hexagon. Find the central angle.
You can insert the information you have straight into the formula and find the answer (just look at the figure above):
Formula
The interior angle of a regular polygon is the angle between two neighboring sides.
The interior angle of a regular polygon with sides can be found with the equation
This is a regular pentagon:
Example 2
You have a regular pentagon. Find the interior angle.
You can insert the information you’ve been given straight into the formula and find the answer:
Formula
The sum of angles in a polygon with sides tells you the sum of the interior angles in the polygon. It’s described by this formula:
Example 3
You have a regular heptagon. Find the sum of its angles.
As a heptagon has seven sides, you can just insert the information you’ve been given into the formula to find the answer: