Question

Finding Angle Relationships
Two parallel lines are cut by a transversal and form a pair of alternate exterior angles. One angle measures (6x + 5)° and the other measures (7x – 4)°. Explain how to determine what those angles actually measure?

Answer 1

Alternate exterior angles formed by a transversal of parallel lines are congruent, so set them equal:

6x + 5 = 7x − 4
5 + 4 = 7x − 6x
9 = x

Now substitute x = 9 into either expression:

6(9) + 5 = 54 + 5 = 59°
7(9) − 4 = 63 − 4 = 59°

So x = 9 and each alternate exterior angle measures 59°.