A polygon is a shape with three or more straight sides.

### Types of Polygons

A

convexpolygon has no interior angles greater than 180°

A concave polygon has one or more interior angles greater than 180

°.A regular polygon has all sides and all angles equal.

e.g. a regular hexagon.

### Angles of Polygons

The exterior angles of any polygons add up to 360**°**.

e.g. a + b + c + d = 360

^{o}

The interior angles of a polygon have different sums depending on the number of sides in the polygon.

**For a polygon with n sides:** **the sum of the interior angles = (n − 2) x 180 °**

e.g. For a 5-sided polygon (called a pentagon)

the interior angles add up to ( 5 − 2) x 180^{ }= 540°

- Each polygon can be split into triangles:Three triangles can be drawn.

Total interior angles of three triangles = 3 x 180**°** = 540^{o}

### Regular Polygons

The table summarises the names and angles of the more common regular polygons.

Number of sides |
Name |
Size of each exterior angle |
Size of each interior angle |

3 |
180 − 120 = 60 |
||

4 |
180 − 90 = 90 |
||

5 |
180 − 72 = 108 |
||

6 |
180 − 60 = 120 |
||

8 |
180 − 45 = 135 |
||

10 |
180 − 36 = 144 |
||

n |
n − gon |
180 − |

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