

Triangle Tilings: Nice Angles 

We use the term nice angle to refer to angles which are 180/n
degrees for some whole number n. So the nice angles are (in degrees)
180/2 = 90, 180/3 = 60, 180/4 = 45, 180/5 = 36, 180/6 = 30, 180/7 =
25.714..., 180/8 = 22.5, 180/9 = 20, and so on (there are infinitely
many). It turns out that in order for a triangle to fit evenly into a
tiling the angle at each of its corners must be a nice angle. This
is so that an even number of the triangles will fit around that corner.
For example, if a triangle has a 90 degree angle, then 4 copies of that
triangle will exactly fit around that corner.


