Understand the Angle Relationships in Polygons

In this activity, we will look at the relationship of the angles inside and outside polygons. 

 

A polygon  - A 2D shape bounded by straight sides.

A regular polygon - All the angles are the same and the sides are the same length.

 

Exterior angles (outside angles)

As we know, the exterior angles add up to 360^o

 If they slide into the middle of the shape to a point, we can see that they add up to 360^o

 

 

 

We can work out the exterior (outside) angle by:

360^o ÷ number of sides = exterior angle

So, for a pentagon: 360^o ÷ 5 sides = 72^o

 

Interior angles (inside angles)

 

 

We can see from the diagram that the exterior angle and the interior angle form a straight line.

We know that a straight line adds up to 180^o

To find the interior angle we can do:

Interior angle = 180^o -  exterior angle

For a pentagon: interior angle = 180^o -  72^o

Interior angle = 108^o

 

Let's try some questions using these facts!