In math books, it is common to find statements that the right angle measures 90 degrees and the shallow angle measures 180 degrees. But what is the reason for the values being precisely 90 and 180?
In the year 4000 BC, when Egyptians and Arabs tried to work out a calendar, it was believed that the sun revolved around the earth in an orbit that took 360 days to complete one revolution. Thus, each day the sun traversed a portion of that orbit, that is, an arc of circumference of its orbit.
This arc was matched by an angle whose vertex was the center of the earth and whose sides passed through the ends of such an arc. So this angle became a unit of measure and was called the degree or one degree angle.
Next: History of Combinatorial Analysis
Thus, for the ancient Egyptians and Arabs, the degree was the measure of the arc that the sun traveled around the earth for a day. Today we know that it is the earth that revolves around the sun, but tradition has been maintained and it has been conventionally said that the arc of circumference measures one degree when it corresponds to 1/360 of that circumference.