Find the Missing Angle

Reflection:

The task aligns with the Standard of Mathematical Practice 7 of looking for and making use of structure. The task provides information in which students must be able to apply to break the task down into smaller angles and shapes to further solve. The task requires students to apply previous theorems and postulates relating to triangles and parallel lines in order to solve. I found this task very fun to solve as I was able to visualize several different methods to solve once I had created a transversal line between the parallel lines.

Students could be challenged by this task if they not extend line PB to reach the other parallel line. The transversal line is essential to include to further see the relationship between the given angles or the triangle that is created. There are several different methods to solve this task depending on the postulate and theorems that students have a better understanding of.

This task would be great as a review or exploratory problem in my Geometry course as it ties several concepts together in order to solve. The task could be used as an exploratory problem prior to discussing triangles and extended into asking students what relationships they see between the exterior and interior angles in the triangle. It could be used as a review of the different angle relationships given parallel lines as students must create a transversal line, which aids in starting all students the problem. It could be extended by having students find multiple solutions to review and build together the theorems and postulates discussed throughout the course.

Source: http://tasks.illustrativemathematics.org/content-standards/8/G/A/5/tasks/56