We know that the right angle measures 90º and the shallow angle measures 180º. But why are the values 90 and 180?
In the year 4000 BC, the Egyptians and Arabs tried to work out a calendar. At that time, it was believed that the sun took 360 days to complete orbit around the Earth. Thus, each day the sun traveled a little bit of this orbit, that is, an arc of circumference of its orbit. This angle became a unit of measure and was called the degree.
So for the ancient Egyptians and Arabs, the degree was the measure of the arc that the sun traveled around the earth for a day. However, 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.