360/Historical Note

Historical Note on $360$ (Three Hundred and Sixty)
There are $360$ degrees in a full angle.

This appears to have been first done by.

$360$ is very approximately equal to the number of days in a year, which goes some way towards explaining this division of the circle.

Each of the signs of the Zodiac were divided into $30$ degrees, each one corresponding to approximately one day's travel of the sun around the ecliptic.