You already know that the interior angles of a triangle add up to 180º.
Polygons with more sides have a larger sum of interior angles.
To work out the sum of the interior angles of a polygon with more sides, we choose one of the corners and split the polygon into triangles. Each triangle will contain 180°.
Work out the sum of the interior angles of this hexagon.
Choose any one corner.
Draw diagonals from the chosen corner to form triangles.
There are 4 triangles inside the hexagon.
4 x 180° = 720°
The sum of the interior angles of a hexagon is 720°.
When you have a shape with n sides, the number of triangles it can be split into is n-2
Once you have the number of triangles, we can simply multiply that by 180° to find the internal angles.
For example: A 5 sided shape can be split into 3 triangles, if you then multiply 3 by 180 you get that there are 540° in a 5 sided shape.