9.06 Angles of polygons

Review of 2D shapes

Regular

A regular polygon has all sides (and angles) equal length and size. 

These are all regular polygons.

 

Irregular

An irregular polygon has some sides (and angles) of different lengths and sizes.

These are all irregular polygons.

The word polygon comes from the Greek poly - meaning many and gonos - meaning angles.  So a polygon is a many angled figure.  

With many angles comes many sides, in fact, every 2D straight-sided shape has the same number of angles as sides.  

 

 

Naming 2D shapes

Different sided figures have names that describe the number of angles and sides.  

          

          

           

          

 

Sum of interior and exterior angles of 2D shapes

Angle sum of an n-sided polygon is $\left(n-2\right)\times180$(n−2)×180 degrees The angles inside a quadrilateral will add up to $\left(4-2\right)\times180=360$(4−2)×180=360 degrees The angles inside a hexagon will add up to $\left(6-2\right)\times180=720$(6−2)×180=720 degrees The angles inside an octagon will add up to $\left(8-2\right)\times180=1080$(8−2)×180=1080 degrees
Sum of exterior angles of any polygon is $360$360°

 

Practice questions

Question 1

Question 2