Degrees are very natural in the context of ancient astronomy/astrology, where you have (1) ~365 days in a year, so that if you look at the path of something that takes a year you get about one degree change per day but with a number that is more easily divisible. (2) approximately 4y, 10y, 8y, 15y, 12y, 30y cycles for the moon and various planets. (3) A calendar with 12 months, 12 zodiac signs. (4) A timekeeping system which breaks days into 24 hours and then uses divisions by sixty for smaller units. (4) A base-sixty number system – from ancient Mesopotamia, which persisted as the standard for astronomical calculations for millennia, only displaced in the very recent past.