During the French Revolution, they tried to make a right angle have 100 degrees and even recomputed all new trig tables for this new standard. It obviously did not catch on :)
It's a degree scale: you can choose any number you want.
(720720 might be OK too so we can cut 16 pieces, but honestly, if you're cutting 16 pieces, you're not going to measure. You're just going to divide pieces in half until you have 16. 360360 is the future.)