1. Angles in Polygons

2. Interior and Exterior Angles
This is a regular pentagon.
By extending each side we can see the exterior angles

3. Interior and Exterior Angles
All the exterior angles can fit around a point, as follows:
This means that the exterior angles
on a polygon add up to 360°

4. Interior and Exterior Angles
The interior angles on a polygon are on the inside!
interior and exterior angles
Notice that the
make a straight line
That means:
int + ext = 180°

5. Calculate the exterior angle and interior angle on a regular octagon.
Example:
Calculate the exterior angle and interior angle on a regular octagon.
sum of exterior angles = 360°
360 8
exterior angle = = 45°
int + ext = 180°
int + 45 = 180°
int = 135°

6. Investigating the sum of interior angles on any polygon

7. Name of polygon
Number of sides
Number of triangles
Sum of interior angles
Triangle 3 1
1 × 180 = 180°
Quadrilateral 4 2
2 × 180 = 360°
Pentagon 5
3 × 180 = 540°
Hexagon 6
4 × 180 = 720°
Heptagon 7
5 × 180 = 900°
Octagon 8
6 × 180 = 1080°

8. Interior and Exterior Angles
The sum of
interior angles in
any polygon is
calculated by...
Sum int = (n-2) × 180
where n is the number of sides on the polygon

9. Find the sum of interior angles on a dodecagon.
Example:
Find the sum of interior angles on a dodecagon.
A dodecagon = 12 sides
Sum int = (n - 2) × 180
Sum int = (12 - 2) × 180
= 1800°

10. Example: Sum of int = (n – 2) × 180 = (5 – 2) × 180 = 3 × 180 = 540°
75°
140° 2x 3x
3x + 5
75°
140° 2x
Sum of int = (n – 2) × 180
= (5 – 2) × 180
= 3 × 180
= 540°
2x + 3x x = 540°
8x = 540°
8x = 320°
x = 40°