2. Looking at the Consecutive Interior Angles (9 points)

Look at the diagram of the scenario below. A steep downhill ski slope is intersected at an angle by a less steep ski slope. Safety fences need to be set up in the locations shown. The angles of the fences, angles 1 and 2, can be determined by finding the relationship between the angles a and b.

1. Draw a geometric diagram of this scenario using two parallel lines and one transversal. (Remember that a transversal is a line which cuts across parallel lines.) Label the angles, parallel lines, and transversal as indicated in the diagram above. (2 points)
3. Starting with the fact that angles 1 and a are a linear pair and that angles b and 2 are also a linear pair, use a two column proof to prove that consecutive interior angles a and b are supplementary. (5 points)