Its just defined as that, there is no mathematical trick to it. And there is other units like radian that do not work on the 360 base.
And 360 is a nice number to divide, its divisible by 2, 3, 4 ,5 ,6 and much more. So like the clock thats in some multiple of base 6 too, we addopted this system from the mayans i think.
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