For this problem, be sure to tear, not cut, the three angles off the triangle. This way you will be sure which point is the angle under consideration. If you cut them, you will end up with three clean-cut points (angles), and it is easy to become confused about which are the actual angles of the triangle.
This approach for justifying that the sum of the angles in a triangle is 180 degrees is an informal justification or proof. A more formal proof can be written using what you know about the angles formed when parallel lines are cut by a transversal, which will be explored next.