https://en.wikipedia.org/wiki/Degree_(angle)#History
Summary: We don’t know for sure. It might be because early applications of circles were largely for astronomy, and a year is 365 days long (which with early inaccurate methods of measurement meant some calendars were 360 days long). 360 is also fairly easy to work with, because it has so many divisors. It perhaps just got taught onwards from there because no alternative was obviously better.
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