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A polygon is a shape with three or more straight sides.
A regular polygon has all sides and all angles equal.
e.g. a regular hexagon.
Angles of Polygons
- The exterior (outside) angles of all polygons add up to 360°.
e.g. a + b + c + d = 360o
- The interior (inside) angles of a polygon have different sums depending on the number of sides in the polygon.
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 |
360⁄3 = 120° |
180 − 120 = 60°
|
| 4 |
Square |
360⁄4 = 90° |
180 − 90 = 90°
|
| 5 |
Pentagon |
360⁄5 = 72° |
180 − 72 = 108°
|
| 6 |
Hexagon |
360⁄6 = 60° |
180 − 60 = 120°
|
| 8 |
Octagon |
360⁄8 = 45° |
180 − 45 = 135°
|
| 10 |
Decagon |
360⁄10 = 36° |
180 − 36 = 144°
|
| n |
n − gon
|
360⁄n |
180 − 360⁄n
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Constructions 
To construct a regular polygon, use a circle and divide 360° by the number of sides of the polygon
being drawn.
See construction
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