How to Solve Parallel Lines and Transversals Problems? (+FREE Worksheet!) Parallel Lines and Transversals - Example 1: In the following diagram, two parallel lines are cut by a transversal. What is the value of \ (x\)? Solution: The two angles \ (3x-15\) and \ (2x+7\) are equivalent. That is: \ (3x-15=2x+7\) Now, solve for \ (x: 3x-15+15=2x+7+15 →\) \ (3x=2x+22→3x-2x=2x+22-2x→x=22\)