Parallel lines - lines that will never cross over one another. They also share the same slope. (Remember slope?)
Transversal - a line that crosses over two or more lines at only one point each
The idea is that if a pair of parallel lines has a straight line that crosses them both, that line will create the same angle measurements in both parallel lines. But the angle measurements will only appear in similar positions in each parallel line. This is called corresponding angles (remember corresponding sides?)
From there, you can use alllll that you know about vertical angles, adjacent complementary, and adjacent supplementary angles to find all the measurements for these parallel lines when they're crossed by a transversal line.