Do you mean "on the fly" (during your pre-shot routine)?
If so, "product of halves" is probably the best compromise of convenience and accuracy:
You know the straight-in line (0-degree) and can pretty easily visualize the 90-d line. Cut that angle in half and you're at the 45-d line. Half again gets you to the 22.5-d line (67.5-d line on the "other" side of the 45-d line). Half again is 11-d. You can keep cutting by halves but at this point you can probably come up with a very close estimate since you're in the ballpark already.
Do this for every shot for a couple hours and it will become second nature.
But what's the use? If aiming, there are better/easier ways to aim than figuring out the cut angle degree and CB-OB overlap for a shot.
Visualize the line from center of object ball to desired point of impact(usually pocket) and a second line(tangent line) at 90 degrees to the first line. Visually bisect(divide by 2) the 90 degree angle formed by the 2 lines using your cue as a guide if necessary and you will have the 45 degree line. Look to see where your cue ball lies in position to the 45 degree angle line and you can make a quick guess at the angle of the shot. You can also bisect the 45 degree angle on either side and end up with a 0, 22.5, 45, 67.5 and 90 degree reference lines to estimate the angle. It shouldn't take long before you brain can quickly determine the angle of the shot within a couple degrees by just looking looking at it.