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

regular polygon has all sides and all angles equal.

e.g. a regular hexagon.Y8_Polygons_02.gif


 

Angles of Polygons

 

  • The exterior (outside) angles of all polygons add up to 360°.

e.g. a + b + c + d = 360oY8_Polygons_03.gif

  • 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
3603 = 120°

180 − 120 = 60°

4
Square
3604 = 90°

180 − 90 = 90°

5
Pentagon
3605 = 72°

180 − 72 = 108°

6
Hexagon
3606 = 60°

180 − 60 = 120°

8
Octagon
3608 = 45°

180 − 45 = 135°

10
Decagon
36010 = 36°

180 − 36 = 144°

n

n − gon

360n

180 − 360n

Constructions ShapeArt.8.jpg

To construct a regular polygon, use a circle and divide 360° by the number of sides of the polygon
being drawn.

See construction