Question

Find the value of x for which m parallel to n A. 31 B. 33 C. 39 D. 41

Answer 1

Hello!

We are told that n and m are parallel.
The angle that measures 105 degrees is supplementary with the alternate interior angle of the angle which measures (3x - 18) degrees. Supplementary angles add to equal 180 degrees, so we can make an equation by first finding the measure of the alternate interior angle.

180 - 105 = 75

The alternate interior angle measures 75 degrees, so we can set that equal to 3x - 18 to solve for x since alternate interior angles are congruent.

75 = 3x - 18
93 = 3x
31 = x

Answer:
x = 31