If you stack these angles cleverly, you and add and subtract, thus getting you:
45-30 = 15 degrees
60-45 = 25 degrees
30+45 = 75 degrees
In general, you will encounter angles at 30/45/60 degrees, but other angles are possible, just not as as likely.
This doesn't mean that you won't get other angles. There's no enforcement angel slapping an architect's hand every time that they make an unusual decision.
A second way to create an angle is to locate intersection points and connect the dots. When this happens, it's up to you to figure out the exact methodology. Because this is drafting, there must be a methodology, so don't give up easily.
Finally, professional architects and engineers have drawing arms which twist around to any possible angle. If they want an angle, they will get it. From my observation, that sort of measuring generally wasn't used in Art Deco as it violates the principal of relationships. When I have trouble figuring out a drawing, I dig deeper, and somewhere back there is a primary geometric relationship, not an arbitrary decision.
Return to: Art Deco 101
Douglas Milewski is a fantasy writer who liked drafting class too much. In his recent artistic struggles to produce art deco for his own covers, he found no internet sites dedicated to the technical underpinnings of the art. Seeing a niche that needed filling, he has documented his hard learned experiences. He doesn't claim that he's right, and would very much appreciate it if someone more competent would save him from his own folly.