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?

Alternate exterior angles, when parallel lines are cut by a transversal, are congruent. Therefore, the angles are equal...so set them equal.

6x + 5 = 7x - 4...now we solve for x
6x - 7x = -4 - 5
-x = -9
x = 9

one angle (6x + 5) = 6(9) + 5 = 54 + 5 = 59 degrees
other angle (7x - 4) = 7(9) - 4 = 63 - 4 = 59 degrees
as u can see, they are both congruent and they each measure 59 degrees