To make uncommon angles you will need some rudimentary knowledge of trig. As explained below by huck finn.
But for common angles you can use a ruler, for example, a triangle that has a 3" side, 4" side and a 5" side, it will always form a 90deg angle. (this same triangle can come in larger sizes like [6,8,10], [9,12,15], [12,16,20], etc)
Or a triangle with equal sides ([1,1,1], [2,2,2], [6,6,6], etc) will have all angles at each corner equal to 60deg.
There are many more. It comes down to memorizing the ones you need for the common angles. Most engineers know better than to give out uncommon angles without a protractor or instructions on how to measure the angle.
Students to the math teacher: "When will we ever use this stuff?"
Drew