Before you pick up a compass or protractor, familiarize yourself with the 90- and 180-degree angles that you find in everyday life. Once you have a grip on those angles, you'll be able to cope with everything in between much more easily.
Think of a 90-degree angle as the corner of a perfect square. Maybe you've helped someone with a woodworking project and used a T-square tool to ensures that a corner measures a perfect 90 degrees. Or, think of how a clock face looks when the hands are pointing to 3:00. They form a 90-degree angle (and at 9:00, too!).
Ever heard the expression to "do a 180-degree turn" about some topic? The phrase means to completely change one's opinion from one thing to the complete opposite. In terms of angles, each ray of a 180-degree angle points in exactly the opposite direction. In other words, this angle is so wide open that it looks just like a straight line. Think of a book laying flat open on the table, or picture how that clock face looks at 6:00.
Once you have those two angle shapes firmly in mind, you can begin to grasp the other angles with values in between. If you know that 180 degrees is like a flat open book, you can visualize an angle greater than 180 degrees by opening the book even more so that the covers begin to push together (but don't break the binding!). If you were to close the book so that it's open only a tiny crack, you have a small angle of less than 90 degrees.