I continue to be tempted by the Angle Cube. Perhaps one day, with a little mirror. How fast does it respond? A freehand stroke is under a second somewhere, but at least it might show slow "drift" in freehand angles.
At least for me, better than the folding-paper approach is the ruler method -- measure the width of the blade ("width") and then the height of the center of the spine off the stone ("spine") gives the angle, within about a degree for the angles we are talking about and without a fancy calculator, as
angle ~ ( spine / width ) x 60°
- 1 in 4 ~ 15°
- 1 in 5 ~ 12°
- 1 in 6 ~ 10°
- 1 in 10 ~ 6°
An example -- 48 mm high gyuto, 1-in-6 angle gives 48/6 = 8 mm to raise the center of the spine off the stone for about a 10° half-angle.
Even if the angle isn't exact, it is repeatable,
which is what is usually important. I generally don't care if I am sharpening to exactly
12° but I do care that, for example, last time I sharpened the edge didn't last as long as I wanted, so I want a little bigger angle this time.