The one thing that the unit of "degrees" has going for it is that it tends to give integer answers (because 360 is so divisible). If you convert them into rotations around a circle, they angles become (1/6, 3/8, 7/24, 1/4, 5/12). (Multyply those by τ=2π to get the angle in radians).
EDIT:
To your question as to why angles can't be to weird, consider vertices, where the corners of the pentagons meet. Each vertex is composed of three angles, one from each of the three neighboring vertices (although it is not a-priori obvious that a vertex contains only three angles). The sum of these angles (in rotations) must be 1. This means that, heuritstically, you would want as many permutations of the angles as possible to add up to one.
EDIT:
To your question as to why angles can't be to weird, consider vertices, where the corners of the pentagons meet. Each vertex is composed of three angles, one from each of the three neighboring vertices (although it is not a-priori obvious that a vertex contains only three angles). The sum of these angles (in rotations) must be 1. This means that, heuritstically, you would want as many permutations of the angles as possible to add up to one.