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

Pick a point in the middle of one side of an n-sided polygon. Without changing anything else, declare that point to be a “corner”, so now you have an n+1-sided polygon. The “corner” you just added has 180 degrees. If you squish the new polygon around so that your corner actually bends to less than 180 degrees, the other corners open up so the total angle remains unchanged.