The worksheet first guides students through step-by-step instructions of how to copy an angle using only a compass and straightedge.
Then, on the back, students are challenged to use this to construct a line that's parallel to a given line and passes through a given point. This is left open-ended for the students to figure out.
The goal of this exercise is to have students experience Euclidean constructions and apply what they know about angle pairs to make parallel lines. (I do this after my lesson about corresponding angles, alternate interior angles, etc.)
In addition, constructions appear in the common core standards (and on the PARCC test if your state has adopted that).
This zipped file contains the activity as a Word document (in case you'd like to edit it), as well as a PDF.