Find Missing Angles Using the Rules of Polygons

In this activity, we will be looking at angle problems involving the rules of polygons.

Let's recap what we know already!

A regular polygon  - has sides that are all the same length and angles that are all equal. 

Make a note of the following formulae for regular polygons: 

Exterior angle = 360º ÷ number of sides

So with the octagon, each exterior angle is 360 ÷ 8 = 45º

Interior angle = 180º - exterior angle

So, with an octagon, the interior angle is 180 - 45 = 135º

Sum of interior angles = 180 x (number of sides - 2)

So with an octagon, the sum of the interior angles is 180 x (8 - 2) = 180 x 6 = 1,080º

Let's have a look at a typical question using this information.

Example

A regular polygon has an interior angle of 165.6º

How many sides does it have?

Answer

Exterior angle = 180 - interior angle = 180 - 165.6 = 14.4º

Number of sides = 360 ÷ exterior angle = 360 ÷ 14.4 = 25

So this regular polygon must have 25 sides.

Let's have a go at some questions now.