Hi seasdes,
I am not quite sure I understand the question. Angle is a slope differential between at least two vectors (or two lines - remember X is also considered an implicit line).
Probably what you mean is "How do I find the angle of a line to UCS axis X"? or "How do I calculate the projected first angle of intersection beween a line and an arc"?
In the first case, the most obvious answer in all cases would be an angular dimension. The progeCAD "list" command will also display the angle of a single line to the UCS as "Angle in UCS XY plane".