How Close to Perpendicular Can You Get? Open Middle Challenge

Creation of this resource was inspired by this Open Middle problem submitted by Shelli Foust and Robert Kaplinsky.


Using the digits 1-9 at most one time each fill in the coefficients of the three linear equations to the right so that any two lines are parallel and the third line is a transversal that passes through the other two. Note: There are several possibilities!


Repeat the task above, yet this time try to get the transversal (not parallel to the other 2 lines) as "close to perpendicular" to the other two parallel lines as possible! How close to 90 degrees can you get the transversal to intersect the other 2 parallel lines?