My interior design company is called 999. The police thought it was an inside job.

Before I get to do the interior design, architects and builders have been there first. They love angles as it helps them a great deal in their work. They would need to know how to find interior angles of various shapes.

A polygon is any shape with straight sides. A regular polygon has all sides and angles the same, an irregular polygon has different side lengths and angles.

Lets see how this is done.

We know that a triangle has angles that add up to 180°

Did you know that we can use this to help us find the sum of the angles in any polygon?

As you can see we can split a quadrilateral into two triangles. Each triangle has angles that add up to 180°, therefore 180° + 180° = 360°

Here you can see that we can split a pentagon into 3 triangles. Therefore, 3 x 180° = 540°

Can you spot the pattern?

4 sides = 2 triangles x 180°

5 sides = 3 triangles x 180°

Can you see that the number of triangles is two less than the number of sides?

__We can make a formula from this.__

The sum of the degrees in a polygon = number of sides - 2 x 180

Therefore for a hexagon (6 sided shape) we don't need to draw the shape.

6 - 2 = 4. 4 x 180° = 720°

If we know the sum of the angles in a polygon, how do we find the size of one angle?

All you do is take the sum of all the angles ÷ by the number of sides.

Example

The interior angle of a pentagon is 540° ÷ 5 = 108°

And finally

If you are given an interior angle you can find the number of sides like this

Interior angle = 150°

180 - 150 = 30

360 ÷ 30 = 12 sides