An angle in the bend
This problem involves angles in parallel lines.
When posed with this type of problem, many students have difficulty knowing where to begin. Once they are introduced to the notion of adding lines to the diagram, there are a number of different options which lead to a solution.
It is valuable to explore the merits of each strategy with the class. An interactive file of the Angle in the Bend problem is provided on Geogebratube.
Allow your students time to talk about the problem and develop a reasoned solution before requiring them to write a formal proof.