How_To_Be_Good_At_Math

GEOMETRY • CALCULATING THE ANGLES IN A POLYGON 247

Look at this pentagon. You

can see that we can divide

the five-sided shape into three

triangles.

We know that the angles in

a triangle add up to 180º.

The pentagon is made of three

triangles, so the angles add up

to 3 × 180º, which is 540º

Counting triangles

Polygon poser

Combine what you’ve learned about angles inside a

polygon to work out the seventh angle in this irregular

heptagon. Remember, if you know how many sides a

polygon has, you can work out the sum of its angles.

TRY IT OUT

Using a formula

65º

225º

95º

A pentagon can be split

into three triangles

Calculating the

angles in a polygon

To find the sum of all the angles inside a polygon, we can either

count the triangles it contains, or use a special formula.

Here's a rule about the angles

in polygons: the number of

triangles a polygon can be divided

into is always two fewer than the

number of its sides.

So, we can write the sum of the

angles in a pentagon like this:

(5 − 2) × 180°= 3 × 180° = 540°.

Let's look at the pentagon again.

It has five sides, which means it

can be divided into three triangles.

There's a formula that works

for all polygons. If we call

the number of sides n, then:

SUM OF ANGLES IN A POLYGON

= (n-2) × 180°

170º

140º

Answer on page 320

?

246_247_Angles_inside_polygons.indd 247 29/02/2016 18:05