Note1 (sum of angles in a polygon)

 Sum of Angles in a Polygon

The sum of the angles in a polygon depends on the number of edges and vertices. There are two types of angles in a polygon - the Interior angles and the Exterior Angles. Let us learn about the various methods used to calculate the sum of the interior angles

Types of Polygons

Polygons are classified into various categories depending upon their properties, the number of sides, and the measure of their angles. Based on the number of sides, polygons can be categorized as:

Triangle (3 sides)

Quadrilateral (4 sides)

Pentagon (5 sides)

Hexagon (6 sides)

Heptagon (7 sides)

Octagon (8 sides)

Nonagon (9 sides)

Decagon (10 sides) and so on

Based on the other properties, polygons can be categorized as:

Regular Polygons and Irregular Polygons

Concave Polygons and Convex Polygons

Equilateral Polygons and Equiangular Polygons

Types of Angles in a Regular Polygon

A regular polygon is a polygon in which all the angles and sides are equal. There are 2 types of angles in a regular polygon:

Interior Angles- The angles that lie inside a shape, generally a polygon, are said to be its interior angles.

Exterior Angles- An exterior angle of a polygon is the angle between a side and its adjacent extended side.

To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘.

Here n denotes the number of sides of a polygon.