There are a lot of ways to measure an angle. The most common three devices used to measure angles are a protractor, a hand square, and a compass. Protractors are generally metal or plastic and are in the shape of a half moon. A hand square looks like a protractor except is in the shape of a triangle and has straight edges. A compass is metal and is used by putting a pin in place and twisting the attached compass pencil around the pin to draw a measured perfect circle.