# Angles in polygons

**Polygons**

A **polygon** is a **2-D** shape made from **line segments** which enclose a **region**. The end points are called vertices of which one is called a vertex. There are three types of polygons:

- Regular – all sides and angles are equal
- Convex – the sum of all angles is less than 180°
- Concave – some of the interior angles are more than 180°

The names of polygons are as follows:

- Triangles – 3 sides
- Quadrilateral – 4 sides
- Pentagon – 5 sides
- Hexagon – 6 sides
- Heptagon – 7 sides
- Octagon – 8 sides
- Nonagon – 9 sides
- Decagon – 10 sides

**Interior angles in polygons**

The angles inside a polygon are called **interior angles** and the sum of the interior angles of a polygon is as follows:

- Triangle – 180°
- Quadrilateral – 360°

To work out the interior angles of a polygon, the following formula is used:

(*n *– 2) x 180° (*n* is the number of sides for a polygon)

For example:

A square has 4 sides, therefore it has the following interior angle:

(4 – 2) x 180° = 360°

**Exterior angles in polygons**

When working out the exterior angles of a polygon, the following formula is used:

180(*n* – 2)° (*n* is the number of sides for a polygon)