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

Adding a side to a shape is the equivalent of adding another triangle somewhere along its perimeter. The new triangle has angles that sum to 180.