1. It is close to the number of days in a year.
2. The Babylonians believed that at the time of the equinox march and September when day and night equals 12 hours that from the very first ray of sunlight until the disk of the sun left the horizon equalled 1/360th the time the earth remained in daylight 12 hours.
The diameter of the sun is 1/2 of a degree and there are 180 degrees in half a circle so it makes sense.
3. The ancients could have also invented a system for measuring time by observing this perhaps by letting a cup fill with water during the time the sun took to rise 2 minutes.