Say we extend a line from the center-point of the circle out to the edge. That would be the radius. Do that a few more times until you get 24 triangles. Each of the triangles would have the same angle near the center which would widen the further away from the center you get. Now, picture someone living on that flat disc looking at a Sun moving in a circular pattern above themselves. Close to the center, the Sun's angle would change by a certain amount, but the FURTHER AWAY FROM THE CENTER YOU GET, THE LARGER THE ANGLE BECOMES!!!!!

There is NO WAY the Sun's angle would change by the SAME amount regardless of your position since at the edge, the angle would be more obtuse than near the center. 15 degrees in NY would be 80 degrees (or more) at the tip of South America.
@xCivicx
And these are my words