Sum of Interior Angles of a Polygon

Every polygon has interior angles and exterior angles, where an interior angle is the one that lies inside the polygon and the exterior angle is the one that lies outside the polygon. The number of angles and their measurements differ from one polygon to another based on the number of sides of a polygon.

For example, a triangle has three interior angles, and its sum is equal to 180°, whereas a square has four interior angles, and its sum is equal to 360°. But the sum of the interior angles of a polygon remains the same whether it is a regular or an irregular polygon.

The formula to determine the sum of the interior angles of a polygon is given as follows:

S = (n – 2) × 180°

Where,

• S is the sum of interior angles, and
• n is the number of sides or number of angles of polygons

Polygon is defined as a two-dimensional geometric figure that has a finite number of line segments connected to form a closed shape. The line segments of a polygon are called edges or sides, and the point of intersection of two edges is called a vertex. The angle of a polygon is referred to as the space formed at the intersection point (vertex) of two adjacent sides.

A polygon is of two types: a regular polygon and an irregular polygon. A regular polygon is a polygon whose all sides and all interior angles are measured the same, whereas an irregular polygon is a polygon whose all sides and all interior angles do not measure the same. And we also have different types of polygons like triangles, quadrilaterals, pentagons, hexagons, etc, based on the number of sides of a polygon. Every polygon has interior angles and exterior angles, where an interior angle is the one that lies inside the polygon and the exterior angle is the one that lies outside the polygon.