I've wondered how much of an angle you can expect to print and stuff like overhangs (like you describe) are a conundrum to me.
Are there just design features which help support it during printing?
The main reason I'm asking is, I really don't like supports if I can get away with it. I think they make the print (for the most part) ugly. It seems you can never get them cleaned up enough for it to look good.
I watched a video the other day of a guy who printed a "screw" (large-ish, comes out looking sort of like an auger). He printed it vertically without supports. It befuddled me a little bit he was able to get the lead portion of the screw to print without any support. I didn't look at it close enough to see if it was angled up from the main shaft so as to support it. I'd suspect the best you could muster would be 45° or less to build on. If you go much over that, it would probably sag.