Table of Contents
Sum of Interior Angles of a Polygon and Formulas
Interior Angles of a Polygon – Formula: The sum of the interior angles of a polygon is the angle at the center of the polygon, multiplied by the number of sides. This is because the angle at the center of the polygon is 360 degrees, and each side is a fraction of that. For example, a pentagon has 5 sides, so the angle at the center is 360 degrees, and each side is 72 degrees. The sum of the interior angles of a polygon is always 360 degrees multiplied by the number of sides.
Sum of Interior Angles of a Polygon Formula
The sum of the interior angles of a polygon is equal to (n-2)*180, where n is the number of sides in the polygon. This formula is derived by taking the sum of the angles in a triangle (180), and then subtracting the angle between any two consecutive sides.
Sum of Interior Angles of a Regular Polygon and Irregular Polygon
The sum of the interior angles of a regular polygon is 360°. Therefore the sum of the interior angles of an irregular polygon is not a fixed number.
A Theorem about Interior Angles
If the sum of the angles inside a triangle is 180 degrees, then the largest angle is 180 degrees.
Sum of Interior Angles of a Polygon with Different Number of Sides:
Therefore the sum of the interior angles of a polygon with different number of sides is 180 degrees.
Sum of Interior Angles of a Polygon Formula Example Problems:
There are many different ways to find the sum of the interior angles of a polygon. One method is to use the formula:
- Sum of Interior Angles of a Polygon = (n-2)*180
- where “n” is the number of sides in the polygon.
- For example, if you have a hexagon with 6 sides, the sum of the interior angles is (6-2)*180 = 360 degrees.
