I've used a sliding T-bevel at times. But it does not tell you what the actual angle is.
As for calculating angles, look up sine, cosine, and tangent in Wikipedia (or ask a resident 9th grader in Trigonometry:thumbsup

to find the equations for calculating angles and lengths of right triangles (adjacent, opposite and hypotenuse). Also use the Pythagorean theorem. Most calculator will calculate sine/cosine and tangent, but you will need to first convert degrees into radians.
But I suspect there are some basic angles used in woodworking and that the more experienced woodworkers in here do not do much angle calculating. They probably just divide a 45-degree or 90-degree by however many parts they need. Or they measure with a T-bevel and cut without worrying about what the exact angle is.
I am no expert.....