Considering a circle (also applies to any closed loop in 2D) to consist of $360^\circ$ is actually convention with the following origin:

The evolution of the calendar system in various ancient cultures had one similarity. They all referred to the motion of the Sun in the sky. The Sun apparently makes a full circle in a year. Most ancient cultures rounded up the number of days in a year to be 360. In the ancient Hindu Vedic calendar system or astrology, there are 30 days in a month and there are 12 months in a year. This inspired the mathematicians to consider the circle to have $360^\circ$. To correct for the discrepancies between the actual 365 days in a year and the 360 days per year in the calendar, they used correctional methods that added an additional month in a certain amount of years.

This convention has lasted for thousands of years for the following reason:

360 is a very convenient number for real-life divisions. For example, 360 is divisible by all the numerical digits from 0 to 9, except for 7. Thus having a circle with a complete angle $360^\circ$^{ }helps us to divide a circle into various parts without writing decimals for the partial angles.

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