Lost again?

Not to worry! The GPS on your phone can help you find your way.

GPS uses angles, including **exterior angles**, to help calculate and create directions.

The mathematics used in GPS is quite complex, but we can learn about some of the basics to get us thinking a bit more like a GPS system.

Let's start by considering what we need to know about **exterior angles** around points and polygons.

Here is a polygon with its exterior angles highlighted:

If we connect them all together, they always fit perfectly around a point:

This means that the exterior angles of ** any** polygon add up to

**360°**.

__How to calculate the exterior angle of a regular polygon__

A regular polygon's **sides** are all the **same length** (e.g. an equilateral triangle). It also means all the **angles** around the shape are equal.

Let's look at an example:

Find the exterior angle of a regular pentagon.

Because the** exterior angles of a polygon** will fit around a point, and we know that angles around a point add up to 360°, we just use this fact, along with the number of sides of the polygon, to calculate any exterior angle. So:

**360° ÷ number of sides = value of external angle**

In this case:

**360° ÷ 5 = 72°**

Hopefully, now you won't get lost!

In this activity, we will calculate the exterior or external angles of polygons with a variety of different sides by applying the rule that all exterior angles in a polygon will add up to 360°.