The reason that a full circle equals 360 degrees (and not a 100 for example) is that 360 is divisible by 24(!) different numbers, while a number like 100 is only divisible by 9 numbers. Thus 360 is a lot easier to work with mathematically.

On a related issue we can also conclude that base 12 is much more practical than base 10. (1/3rd of 12 = 4, 1/4th = 3,...)

Maybe we'd have this system if humans had 6 fingers on each hand