# Angles of a Polygon

### Interior Angles

An **interior angle** or **internal angle** is determined by two consecutive sides.

#### Sum of Interior Angles of a Polygon

If **n** is the number of sides of a polygon:

**S **= **(n − 2) · 180°.**

Sum of interior angles of a triangle = (3 − 2) · 180° = **180º**.

Sum of interior angles of a quadrilateral = (4 − 2) · 180° = **360º**.

Sum of interior angles of a pentagon = (5 − 2) · 180° = **540º**.

Sum of interior angles of a hexagon = (5 − 2) · 180° = **720º**.

# Angles of a Regular Polygon

### Central Angle of a Regular Polygon

The central angle of a regular polygon is formed by two lines from consecutive vertices to the centre point or two radii of consecutive vertices of the circumsribed circle.

If **n **is the number of sides of a polygon:

**Central angle = 360° : n **

Central angle of the regular hexagon = 360° : 6 = 60º

### Interior Angle of a Regular Polygon

The interior angle of a regular polygon is formed by two consecutive sides.

**Interior angle = 180° − central angle**

Interior angle of a regular hexagon = 180° − 60º = 120º

### Exterior Angle of a Regular Polygon

The exterior angle of a regular polygon is formed by one side and the extension of the consecutive side.

The exterior and interior angles are supplementary, that is to say, that add up 180º.

**Exterior angle = central angle**

Exterior angle of the regular hexagon = 60º.