What exactly is it that you're cutting? If not the miter saw, then definitely the table saw can make cuts like that.
The pieces are for a wall mounted jukebox and the angles make the pieces form a rounded front that is typical in these types of projects. The pieces are 15 1/2" long and some of the angles are very small like 7.5 degrees or 9 degrees.
Don't even try it... Making long, accurate cuts with a hand saw can be done, but not with a hacksaw and not without quite a bit of skill.
Not to brag but I'm no slouch with a hacksaw.

I use one every day for work. I decided to try it though to see if it was even possible. I found that a hacksaw did pretty good considering it had been used for cutting out galvanized pipe recently. I reversed the blade and made short even strokes and reset the blade each time rather use a back and forth motion. The big drawback is that the blade binds as I cut deeper in the wood but I relieved that by cutting off segments of the waste side every couple of inches.
The end result was decent considering what I was working with. Before I did it for my actual cabinet, I would either get a new blade or possibly buy a coping saw.
I like the idea of the protractor for what I'm doing. I was just planning to use trig to figure out the angles but the protractor may be a little more accurate.
Thanks for the help
Joel