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

If you think of each shape as being composed of a number of triangles glued together it makes sense. For example a square is two triangles sharing a side. Paste another triangle on to a square and you have a pentagon. Thus the total sum of angles increases by 180 as you progress