Question

In the diagram, two parallel lines are cut by a
transversal, and <1 and <6 do not form any of the kinds of angle
pairs that you have learned. What is a way you can find the
measure of <6 if you know that the measure of <1 is 132"? Explain.

Answer 1

There are a few approaches. One way is to note that angles 1 and 3 combine to 180

angle1+angle3 = 180

132+angle3 = 180

angle3 = 180-132

angle3 = 48

This is also equal to the measure of angle 6. Angles 3 and 6 are congruent when we have parallel lines like this (since they are alternate interior angles).