Hermann Schmidt combined with a squareness gage. Incidentally none of these is worth a hoot for inspection to a known limit without some calibration and traceability to an accepted reference standard.
All Mitch had to do his analysis were some basic machinist measuring tools and a decent milling machine. This got me thinking about how you would go about measuring and repairing a damaged, out of spec angle plate with only basic measuring tools and the machine that you use the plate on. It hardly helps to have angle plates and standards ten times more accurate than the machine you use them on. The basic accuracy of the machine cannot be improved greatly by adding super precision accessories. In another article we will talk about accuracy, precision, repeatability and resolution. If you don't use sound machining practice and check your output you will never produce superior work. Believe it or not I don't think I have ever made an angle plate before so it turned out to be fun and enlightening for me which is just what I like in a good problem.
In the picture above I have the back saw cut edge supported on two gage pins on the more square side of the two ends. The first order of business is to establish two edges that are as parallel as I can make them. We wouldn't want to stray too far from whatever the average is compared to the other surfaces but you have to start somewhere. This is an important point to establish qualified reference surfaces that you can use to build on in the subsequent setups. Against the movable jaw of the vise you see a round rod clamping the angle. This is positioned to make the two vertical edges of the part against the fixed jaw sit in full contact with the jaw face and not have their alignment be influenced by the rough saw cut on the bottom.Incidentally this rod is the handle for a Starrett tap handle that I have been using for this purpose for years. I always feel a little pang of guilt using it this way but in thirty years the handle is no worse for the job. Now Murphy heard me and will cause me to bump an end mill into it and cement the guilt fully.