I believe the correct tool for that is an “Optical Comparator”, but they are not inexpensive.
One approach I’ve seen for measuring angles is to actually make a cut with two diagonals, and two flats, then place rods of a known diameter in them, measure those and then do the trigonometry to determine the angle. This has the advantage of finding the actual angle which the tool cuts.
Maybe there’s something on that in Machinery’s Handbook Guide?
I spent some more time on this tool measuring project, and it looks like a crafty craftsman could add some fixtures, backlighting, screen templates etc. to one of these USB/digital microscopes setups to create an optical comparator.
Here’s a treatise that I worked up. I don’t have time (or need) to do anything more right now.
I’ve also include a Test-Cut Verification Method that doesn’t need any additional equipment and could be useful with a bit of trigonometric manipulation.