but I still cannot for the life of me fathom why whoever wrote the AngleArc Proc thought that drawing a line from the vertex (centre of the 'circle') would be needed.
This is meant for drawing pie charts. Similar to the code shown by jamie, but there is also a canvas-way to do it (rather than using canvas.Handle).
Using [f1] on Angle16Deg of course brought up 'No help available' - naturally, since that is simply a parameter being passed to the Proc. On 'Arc' or 'AngleArc' it did open the LHelp Viewer but I had to use the [search] to find any reference to 'Angle16'. Contrary to my 'hex math' assumption though, it seems '16' is purely arbitrary.
Just scroll down the page opened after pressing F1 on "Arc" or "AngleArc", and you'll see an explanation of the arguments:
Angle16Deg - Angle for the arc segment in 1/16th of a degree
(The text itself is not very clear (it would be better do say: "Angle for the begin of the arc segment..."), but the nature of the "16" is very clear)