Question

Parallel lines are cut by a transversal such that the alternate interior angles have measures of 3x + 17 and x + 53 degrees. The value of x is
9
18
35
71

Answer 1

Well the sum of the alternate interior angles of a transversal cutting parallel lines should be equal to 180'. 
So (3x+17)=(x+53)
3x+17=x+53
Using transposition method-

3x-x=53-17
2x=36
x=36/2
x=18
Hopw i helped!

Answer 2

When parallel lines are cut by a transversal, the alternate interior angles are equal.

3x + 17 = x + 53

Subtract 'x' from each side:

2x + 17 = 53

Subtract 17 from each side:

2x = 36

Divide each side by 2 :

x = 18