It would be best to share it with three friends. Each of you would get a quarter of the pizza and the angel of that quarter pizza would be 90 degrees. So when you are looking at the sky and measuring degrees, you are measuring the amount of sky that would be covered by an angle of that size. Looking at the sky, your pinky finger held at arm's length would cover about 1 degree. When you are on this planet, you measure angles using a protractor.
Most protractors are one half of a circle like the one below.
The often have two sets of numbers so that you can use it to measure angles going in either direction. To measure an angle with a protractor, carefully set the protractor so that the angle vertex is on the little hole or notch in the middle of the flat bottom of the protractor. Make sure that one side of the angle is lined up exactly with the flat line that passes through the zero. The other side should be going under the protractor. Now, read the measure of the angle be reading where the other side goes out from under the protractor.