This video could easily work into a Geometry course, after discussing angle relationships with parallel lines and transversals.  Since this game is not simply a one step problem (like just using alternate interior angles), students will have to problem solve and explore different angle pairs to find the measure of the indicated angle.  By using this Khan Academy Video to open a lesson, you spark students’ interests (technology, games, etc)  which will help engage them in the activity.

After opening the lesson with this video, I would give a couple more examples, including some that are more challenging.  While working through these examples, I would expect students to use proper vocabulary to identify angle pairs, such as corresponding angles, alternate interior angles, same side interior angles, etc.  To reinforce the content, I would also ask students to explain the relationship between these angle pairs, indicating whether they are congruent or supplementary.  By doing this, we support their conceptual understanding as well as their understanding of the basic language and vocabulary.

As the main activity, students would create their own angle game, preferably using a computer program.  Students could then print off several copies of their game and would then swap with others for an informal assessment.   During this time, the teacher could monitor students’ understanding and determine progress towards mastery.

http://www.khanacademy.org/math/geometry/angles/v/the-angle-game