If talking about triangles:
Are you given any angle measurements before hand?
If so, if you have two angle measurements, in order to get the last angle measurement, you would add those two angle measurements up then do 180-that answer to get the last measurement.
If you're given the sides, you can do law of cosines or law of sines.
But if you're talking about a regular angle, you use a protractor to measure the degrees of an angle.