How Can Internal Angles Be Calculated?

Learn how to calculate the interior angles of polygons, such as triangles, squares, pentagons, and octagons. Find the general rule, formula, and examples with diagrams and exercises. Use the formula (n-2) × 180° to find the sum of interior angles for a polygon, where n is the number of sides.

Insider angles are those at each vertex on the inside of a shape, with one per vertex. For a polygon with N sides, there are N vertices. To find the measure of an interior angle of a polygon, subtract 2 from the number of sides, multiply it by 180, and divide it by the number of sides.

To find the sum of interior angles of a polygon, multiply the number of triangles formed inside the polygon to 180 degrees. For example, in a hexagon, there can be n triangles formed inside the polygon. The general rule is: Sum of Interior Angles = (n−2) × 180°. Each angle (of a regular polygon) = (n−2) × 180° / n.

The alternate interior angles theorem states that when a polygon has n sides, the value of the interior angle is (n−2)180∘ n. To find the size of each interior angle, divide the sum of interior angles by the number of angles in the polygon.

The formula (n-2)×180 can be used to find the sum of the interior angles of any polygon, where n is the number of sides in the polygon.