In the diagram below, a transversal intersects line a and b.a) If m∠1 = 2x+30 and ∠5 = 5x ‒ 45, find the value of x that will make lines a and b parallel. b) Tell what definition, postulate or theorem allowed you to solve for x. c) Then, find the measure of each angle.

When two lines are crossed by a transversal, the lines are parallel if the Alternate Interior Angles are equal. 
Alternate Interior Angles in the diagram are 1 and 5; 4 and 8; 2 and 6 and 3 and 7.
If lines a and b are parallel, then angle 1 must equal angle 5. 
If that's the case then 2x+30 equals 5x ‒ 45
Solving 2x+30 =  5x ‒ 45
3x = 75
x = 25
So, when x = 25, the lines are parallel.