1. Angles
in polygons

2. 3 sides 4 sides 5 sides 180° 2 x 180°=360° 3 x 180°=540° 7 sides
Can you see a link between number of sides and number of triangles made in the shape?
7 sides
8 sides
6 sides
5 x 180°=900°
4 x 180°=720°
6 x 180°=1080°

3. n (n-2) The angles in a ____ sided shape will equal ____ x 180
Finding Angles in Polygons n
The angles in a ____ sided shape will equal ____ x 180
(n-2)
To find the sum of the angles in a polygon, take 2 away from the number of sides and multiply by 180

4. Interior and exterior angles
The angles INside are INterior angles
The angles outside are exterior angles

5. INERIOR ANGLES- Divide the total of the angles by the number of sides
EXTERIOR ANGLES=
180 – interior angle

6. Example 1
What is the size of the interior and exterior angles of a 12 sided shape?
12-2=10
10 x 180=1800° (Sum of angles in the shape)
1800 ÷ 12= 150° (size of each interior angle)
Exterior angle = °
= 30 °

7. Example 2
What is the size of the interior and exterior angles of a 16 sided shape?
16-2=14
14 x 180=2520° (Sum of angles in the shape)
2520 ÷ 14= 157.5° (size of each interior angle)
Exterior angle = °
= 22.5 °

8. Example 3
What is the size of the interior and exterior angles of a 22sided shape?
22-2=20
20 x 180=3600° (Sum of angles in the shape)
3600÷ 22= 163.6° (size of each interior angle)
Exterior angle = °
= 14.4 °

9. Questions
ANSWERS
I=140, E=40
I=144, E=36
I=150, E=30
I=156,E=24
I=165.6, E=14.4
Find the exterior and interior angles of a regular shape which has:
9 sides
10 sides
12 sides
15 sides
25 sides

10. Finding the number of sides
The exterior angles of a regular polygon will always add up to 360°, so
360°÷ (exterior angle)= number of angles / number of sides

11. Example 1
A regular polygon has exterior angles which are all 36 °, how many sides does it have
360÷ 36= 10 sides
Example 2
A regular polygon has interior angles which are all 108°, how many sides does it have
180 – 108= 72 (size of exterior angle)
360÷ 72= 5 sides

12. Questions
ANSWERS 8 9 12 16 18
120
1. How many sides does a regular polygon have if it’s exterior angles are: 45 40 30
22.5 20 3
ANSWERS 2. 8 9 12 16 18
120
2. How many sides does a regular polygon have if it’s interior angles are:
150
156
157.5
162
165
168.75