# Nonagons - polygons with 9 sides

Categories: gcse geometry

A nonagon is a flat shape with 9 straight sides.

## Regular and irregular nonagons

A *regular nonagon* is a 9-sided shape where every side is the same length and every corner has the same angle. All regular nonagons have the same shape, like this:

An *irregular nonagon* is a 9 sides shape where not every side and angle are equal. There are many different irregular nonagon shapes, here is an example:

## Name

The name *nonagon* is a combination of the words *nonus* (Latin meaning *ninth*) and *gonon* (Latin meaning *angle* or *corner*).

This is slightly unusual because most polygons use greek numbers in their name. An alternative name for a nonagon is *enneagon*, based on the Greek word *ennea* (meaning nine). This name isn't used very often.

Nonagons are sometimes called *9-gons*.

## Interior angles

The interior angles of a nonagon are shown here:

The sum of these 9 angles is given by the formula:

```
sum of interior angles = (n - 2) x 180
```

Where *n* is the number of sides. In this case, the number of sides *n* is 9, so the sum of the interior angles is:

```
(9 - 2) x 180 = 1260 degrees
```

For a regular nonagon, all the interior angles are equal:

This means that the interior angle of a regular nonagon is:

```
1260 / 9 = 140 degrees
```

## Exterior angles

The exterior angles of a nonagon are shown here:

The sum of the exterior angles of *any polygon* is 360 degrees.

For a regular nonagon, all the interior angles are equal:

This means that the exterior angle of a regular nonagon is:

```
360 / 9 = 40 degrees
```

## Symmetry of regular nonagons

A regular nonagon has 9 lines of symmetry. This means that it can be reflected over each of the 9 grey lines shown here:

A regular nonagon has rotational symmetry of order 9. This means that if it rotated about its centre by a 9th of a full turn, it will map onto itself:

## See also

- Regular polygons
- Interior and exterior angles of a polygon
- Triangles
- Quadrilaterals
- Quadrilateral family tree
- Pentagons - polygons with 5 sides
- Hexagons - polygons with 6 sides
- Heptagons - polygons with 7 sides
- Octagons - polygons with 8 sides
- Decagons - polygons with 10 sides
- Hendecagons - polygons with 11 sides
- Dodecagons - polygons with 12 sides
- n-gons - polygons with any number of sides
- Other types of polygon
- Star polygons

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