Angles are additive. In other words, a whole angle is the sum of its parts. Two 45-degree angles make a 90-degree angle. Two 90-degree angles make a 180-degree angle. A 60 degree angle can be decomposed into two 30-degree angles.
Here are some of the angle problems that students may need to solve. In order to solve them, students need to know that
a straight angle (a straight line) is exactly 180 degrees.
a full circle is exactly 360 degrees.