Angle sum in a polygon
If we know that the angles in a triangle add up to 180°, we can use this fact to work out the total angle sum inside any polygon. This is sometimes called the interior angle sum (interior is just another word for inside - think interior designer!).
If we pick a corner on a polygon and join that corner to each other corner, we form triangles inside. Each triangle has an angle sum of 180°.
For example, in a pentagon, we form three triangles. Each has an angle sum of 180°, so the total angle sum inside a pentagon must be 180° x 3 = 540°.
The angle sums of polygons are as follows:
Triangle = 180°
Quadrilateral = 360°
Pentagon = 540°
Hexagon = 720°
Heptagon = 900°
Octagon = 1080°
The number of triangles is always two less than the number of sides. We can use this to write a general formula linking the number of sides to the interior angle sum: Interior angle sum = (n - 2) x 180.