Can't take credit for this, nor can I prove the physics (you can jump in here any time, Orton), but according to a Tech Tip in the M & M catalog the following should answer the above questions:
"For any size frame weighing 10 lbs:
60 degrees---force on each screw eye = 6 lbs
45 degrees---force on each screw eye = 7 lbs
30 degrees---force on each screw eye = 10 lbs
15 degrees---force on each screw eye = 19 lbs
10 degrees---froce on each screw eye = 29 lbs
5 degrees---force on each screw eye = 57 lbs
2 degrees--force on each screw eye = 143 lbs
Force = 1/2 Weight
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Sine of Angle
When attaching wire to the hanger located on the back of the picture frame, remember that the degree of slack is vital to the success of the job. Wire pulled tighty from side to side will have a pressure of 143 pounds against the rail. Using a lesser degree on the wire will greatly reduce the pressure against the rail. This can help to prevent the frame from breaking and dropping to the floor. The best angle for the wire is 19 degrees. This will place 20 pounds of pressure against the side rail."
I rarely use screw eyes, and I angle the d-rings inward at the same angle as the wire. If the moulding is too narrow, I use one of several other types of hangers. Also, I made up a triangle of foamboard about 20 inches long at a 19 degree angle to use as a guide. For larger frames when I recommend and provide two hooks I include a little printed "Tech Tip" with the hooks indicating why the two hooks, and how far apart to place them to get the 19 degree angle and why. Makes me look smarter than I am.