1. Polygons and angles

2. The interior angles of a triangle sum to 180o
The interior angles of a square sum to 360o
A square can be divided into two triangles
2 x 180o = 360o

3. A pentagon can be divided into three triangles
3 x 180o = 540o
The interior angles of a pentagon sum to 540o

4. How many triangles can an octagon be divided into?
What is the sum of the interior angles of an octagon?
6 x 180o = 1080o
The interior angles of an octagon sum to 1080o

5. Exterior angles are found by continuing one side beyond the shape and measuring the angle between that and the adjacent side
120o x 3 = 360o

6. 360o / 4 = 90o

7. The exterior angles of a shape always sum to 360o - why?

8. If a shape is regular, all the angles will be the same.
A pentagon has 5 vertices
Each exterior angle will be 360o / 5 = 72o

9. A decagon has 10 sides.
What is the sum of its interior angles?
What is an exterior angle of a regular decagon?
A decagon can be divided into 10 – 2 = 8 triangles.
The sum of its interior angles is 8 x 180o = 1440o
An exterior angle of a regular decagon is 360o / 10 = 36o