I am studying gauges for measurements and I can't find the answer to what device I would use to set angles in 2 plates.
Although a photo or diagram or more detailed description would be helpful, you may find what you seek in a machinist's protractor. There are a few different designs, including a few electronic digital models.
I have the above model, but have yet to use it for anything requiring extreme precision. It has a tendency to flex a bit even after tightening the angle lock.
This model appears often in searches and is much more accurate, according to my previous reading via a machinists' email list. Much if the discussion is that the typical home hobby machinist does not require this much precision, as these devices are rather expensive, upwards of US$300.00
Less precise and less expensive, the above type provides perhaps one-half degree accuracy, but does qualify as a possible solution to your question.