Why can't a regular pentagon tile a plane?

Answer 1

A regular pentagon has 5 equal sides and 5 equal angles. If each vertex (corner) is joined by a line to the pentagon's centre there are 5 equal angles at the centre, which total 360 degrees. Therefore each one is 360/5 degrees = 72 degrees. The other angles inside the 5 triangles are equal and must total 180 - 72 degrees = 108 degrees. The "external angles" equal the ones at the centre (72 degrees).

Now, if a regular figure is to tesselate it must have angles which are simple fractions of 360 degrees, like 10 or 15 or 20 or 30, 40. 45, 60, 90, and angles of 72 or 108 degrees are no use for the purpose.