why when we add more side, the sum of the angles go up by 180 degrees

Question

The sum of the angles of a triangle is 180

For a square it’s 360

For a pentagon it’s 540

For a hexagon it’s 720

Why is that?

In: Mathematics

Answer 1

Because when you turn a full circle around a perimeter you do a full 360. Each turn you make deducts whatever you turn from a flat 180, so in total you will have 180x-360 which is the generalization of the cases you mention.