My most successful way of teaching lines and a transversal has been to draw dotted lines connecting the two lines to literally create a box so students can visualize interior and exterior of the 'box'.
I modeled one example on the board and had students give me names to label the angles rather than numbers. Then I just questioned them by saying which people are inside the box but on opposite sides of the transversal, and questions like that. They seemed to do well with it and for the most part did well on the investigation. They struggled the most with corresponding angles but that seems like a pretty common trend.
This investigation asks students to identify angle pairs, then to name them. Then to discover the relationship between them when the lines are parallel. There is one part where students use colored pencils to color the angles.
This investigation is 4 pages along