You calculate the interior angle of any equal sided polygon by subtracting 2 from the number of sides and multiply by 180 and then divide that by the number of sides. For a pentagon: ((5-2)*180)/5 = 108°. Divide that by 2 to get the miter angle for cutting each side : 54°.
I suspect that most segmented rings are even simply for symmetric. Note that the fewer corners, the wider the pieces you make the segments from need to be (or the narrower the maximum ring can be once turned).
--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.
