Arcs in this case are defined by a start point, an endpoint and a central angle (positive angles are counterclockwise, negative angles are clockwise). In each case, we're given two arcs. The endpoint of the first arc is always the start point of the other. I'm trying to find a formula to determine whether the intersection of the two arcs at their shared start/end point is acute. Two examples are shown below.
This is pretty easy to do analytically on a case by case basis, but finding a formula for it has proven elusive. Any help on finding an algorithmic approach to this problem would be much appreciated