The main thing is when we have a transversal across parallel lines we generate a bunch of angles, which they've numbered 1 through 8. Some are the same angles, some are supplementary angles, which means they add up to 180°. So really for math you just need to know whether it's the same or the supplement, which is pretty obvious from the figure.
But here they want us to match the names. I can never remember them but we're given a menu.
∠2 and ∠5 are alternate interior angles. Alternate means on opposite sides of the traversal. Interior means between the parallel lines. Say the mantra: Alternate interior angles are congruent.
∠3 and ∠5 are none of the above. They're supplements but I don't think they have a name. Usually we proceed in two steps. ∠3 and ∠1 are a linear pair so supplementary. ∠1 and ∠5 are corresponding angles so are congruent.
∠3 and ∠8 are alternate exterior angles. Exterior means outside the parallel lines. Alternate exterior angles are congruent.
∠4 and ∠7 are alternate interior angles so congruent.
∠4 and ∠8 are corresponding angles so congruent.
They didn't give an example, but ∠3 and ∠4 are vertical angles, and vertical angles are congruent.
