# Polygon

A **Polygon** is a closed figure made up of line segments (not curves) in a two-dimensional plane. polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides. The sides of a polygon are also called its edges. The points where two sides meet are the vertices (or corners) of a polygon.Polygon is the combination of two words, i.e. poly (means many) and gon (means sides).

## Types of Polygon

Depending on the sides and angles, the polygons are classified into different types, namely:

- Regular Polygon - Polygons that have equal sides and angles are regular polygons.
- Irregular Polygon - Polygons with unequal sides and angles are irregular polygons.
- Convex Polygon - A convex polygon is a polygon with all interior angles less than 180°.
- Concave polygon - A concave polygon is a polygon with at least one interior angle greater than 180°.

**Simple and Complex Polygon:**

**Simple Polygon –** A simple polygon has only one boundary. The sides of a simple polygon do not intersect.

**Complex Polygon – **Complex polygon is a polygon whose sides cross over each other one or more times.

**Sum of Angles of a Polygon : **Sum of the interior angles of a polygon with n sides = (n – 2) × 180°

**Sum of the exterior angles of polygons = 360°**

**Angles in Regular Polygon**

In a regular polygon, all its

- sides are equal
- interior angles are equal
- exterior angles are equal

**Interior Angle: **

Sum of the interior angles of a polygon with n sides = (n – 2) × 180°

So, each interior angles = (n – 2) × 180n

**Exterior Angle:**

Sum of the exterior angles of polygons = 360°

So, each exterior angle = 360°n

**Sum of Interior Angle and Exterior Angle:**

Whether the polygon is regular or irregular, at each vertex of the polygon sum of an interior angle and exterior angle is 180°.

## Properties

The properties of polygons are based on their sides and angles.

- The sum of all the interior angles of an n-sided polygon is (n – 2) × 180°.
- The number of diagonals in a polygon with n sides = n(n – 3)/2
- The number of triangles formed by joining the diagonals from one corner of a polygon = n – 2
- The measure of each interior angle of n-sided regular polygon = [(n – 2) × 180°]/n
- The measure of each exterior angle of an n-sided regular polygon = 360°/n