Angles in Polygons

A triangle's angles total 180°, and everything in this track comes from cutting other shapes into triangles. One diagonal turns a quadrilateral into two of them, which is where its 360° comes from; a fan of diagonals from a single corner turns any polygon into two fewer triangles than it has sides, which is the general formula. Then the same shapes are looked at from the outside, and something unexpected happens: the exterior angles total 360° whether the shape has three corners or a hundred, because walking once round an outline is one full turn however it is divided up. The last tutorial puts both results to work on regular polygons, where every corner is identical and a single number describes the shape — and finishes with the reason only three regular shapes will tile a floor, which falls straight out of the angle formula rather than out of anything about tiles.