## Polygons

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

### Types of Polygons

convex polygon 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 = 360o  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° = 540o

### 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 Equilateral triangle 180 − 120 = 60° 4 Square 180 − 90 = 90° 5 Pentagon 180 − 72 = 108° 6 Hexagon 180 − 60 = 120° 8 Octagon 180 − 45 = 135° 10 Decagon 180 − 36 = 144° n n − gon 180 − 