Have you aver wondered why is a 360 a full circle, I mean it could also be like 180 or 60 degrees so why is it 360?
Our "numbering" system for time and angles originally came from the Babylonians. They had a base number system of 60. One of the reasons is that 60 is divisible by 2, 3, 4, 5, 6, 10 and 12 and etc.
This divisibility means that you don't have to deal with fractions as much (a very difficult thing to do with a non decimal system - think about doing decimal calculations using Roman numerals!!)
So why 360? Well it's not very hard because 6 x 60 = 360.
Another theory was there is more to this than the six sixes for the 360 fromthe Babylonians. It has to do with Claudius Ptolemy (100-170 AD), who divided the circle into 360 parts for his sine table. He actually used the length of the chord for each central angle in steps of 1/2 degree in a circle of radius 60 rather than sines.