How do you find the angle measurement (in a easy explanation)

It really depends on the question.

If you didn't have any information on the surrounding angles, and thus you wouldn't be able to use algebra,

You would find an angle with a protractor.

However, if you were dealing with right angle triangles, (i'm aware you're in middle school), like in highschool, you could find an angle using trigonometry.

It depends. You can find it with a protractor, or if they give you an equation you can just solve for the variable they give you.