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When you’re learning something new, it’s hard to sift what you need to know out of what you assume you need to know. You can spend a lot of time and money on something that doesn’t move you any closer to where you want to be. There are plenty of these traps on the way to becoming an accomplished woodworker, and it doesn’t help the beginner that there are plenty of pundits and purveyors of tools who will gladly lead you down a wayward path. Angles other than 90 or 45 degrees are a good example of this.
The practice of measuring, laying out and cutting angles in terms of degrees is rather new in woodworking. Old woodworking texts discuss angles in terms of rise and run; make a mark a certain distance horizontally and another mark a set distance vertically. Connect the marks with a line, cut and trim to the line and your done. What’s important is that two pieces of wood fit nicely together when assembled. 
The pile of tools in the photo represents a progression of devices used to measure angles. Most of them claim an advantage due to the ability to resolve angle measurements in finer and finer increments. But the one tool that actually gets used is the simple bevel with no numbers at all. The reason for that is it works reliably and accurately, quickly and without confusion. Just because someone can make a device that displays angles in hundredths of a degree, doesn’t mean there is an advantage in using it.
So here’s one of the secrets of what we do when we publish plans in Popular Woodworking Magazine. We draw angles by making marks and connecting lines, when we design with our CAD program and when we work in the shop. If someone wanders by while we’re in the shop and asks us what the angle is in degrees, we give them a lengthy discourse on why they don’t need to know that. Then at the very end, we let our computer measure the angle and we throw the angle measurement into the drawing. Because we know that someone will ask.
