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