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Two reasons. Divisibility was important to ancient mathematicians. 360 is divisible by all numbers to 10, other than 7; plus a lot more larger numbers. The second is that the earth took just around 360 days to orbit the sun.

From a high level of divisibility we have now moved to a situation where, in advanced mathematics, the measure of one full turn is 2*pi, not even a rational number.

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15y ago
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Q: Why are there 360 degrees in one full turn?
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