1. Finding the Sum of a Polygon’s Interior Angles
18 September 2018

2. Poly means many and gon means angles.
The word ‘polygon’ is a Greek word.
Poly means many and gon means angles.
Here are some polygons
Triangle
Pentagon
Octagon

3. How to find the sum of the interior angles – i. e
How to find the sum of the interior angles – i.e. How to find a + b + c + d + e b a c d e

4. How to find the sum of the interior angles – i. e
How to find the sum of the interior angles – i.e. How to find a + b + c + d + e
Split the shape up into triangles

5. Split the shape up into triangles Each triangle contains 1800
How to find the sum of the interior angles – i.e. How to find a + b + c + d + e
Split the shape up into triangles
Each triangle contains 1800
1800
1800
1800

6. Split the shape up into triangles Each triangle contains 1800
How to find the sum of the interior angles – i.e. How to find a + b + c + d + e
Split the shape up into triangles
Each triangle contains 1800
3 x 180 = 5400
1800
1800
1800

7. Split the shape up into triangles Each triangle contains 1800
How to find the sum of the interior angles – i.e. How to find a + b + c + d + e
Split the shape up into triangles
Each triangle contains 1800
3 x 180 = 5400
The sum of the interior angles is 5400
1800
1800
1800

8. Copy and complete this table
Copy and complete this table. Find the interior angles by drawing and splitting up into triangles.
Name
Number of Sides
Sum of Interior Angles
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10

9. Copy and complete this table
Copy and complete this table. Find the interior angles by drawing and splitting up into triangles.
Name
Number of Sides
Sum of Interior Angles
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
900
Octagon 8
1080
Nonagon 9
1260
Decagon 10
1440

10. Regular Polygons
NB. If the polygon is regular, to find an interior angle use the rule:
Interior Angle
1200
Int.Angle = 180 – (360 ÷ n)
n is the number of sides
Int. = 180 – (360 ÷ 6)  180 – 60 =120

11. And Ext. Angle = 180 – Int.Angle
Regular Polygons
exterior angle (180 – 120 = 60
NB. If the polygon is regular, to find an exterior angle use the rule:
Interior Angle
1200
Ext.Angle = 360 ÷ n
n is the number of sides
And Ext. Angle = 180 – Int.Angle