Tiling the plane with congruent polygons

It is impossible to tile the plane with regular pentagons of the same size, because the internal angle of a pentagon is 108°, and 360 is not a multiple of 108. However, it is possible to tile the plane with copies of a pentagon with angles of 60°, 80°, 100°, 140°, and 160°, as shown in the picture above. It is necessary to flip some of the tiles over in…