Lines \( L_1 \) and \( L_2 \) are parallel. The angle between \( L_1 \) and the transversal is 30 degrees. The angle between \( L_2 \) and the transversal is 20 degrees.

Rewrite the information so it makes sense:

Lines \( L_1 \) and \( L_2 \) are parallel. If the angle between \( L_1 \) and the transversal is 30 degrees, what is the angle between \( L_2 \) and the transversal?

In this problem, we have two parallel lines, [tex]L_1[/tex] and [tex]L_2[/tex], that are intersected by a transversal. We are given the angles formed between the transversal and the parallel lines.

The key fact to remember here is that when a transversal crosses two parallel lines, corresponding angles are equal. This means that the angles created by the transversal on one side of the first line match the angles on the same side of the second line.

If [tex]L_1[/tex] makes a 30-degree angle with the transversal, then the corresponding angle on [tex]L_2[/tex] should also be 30 degrees. This is because corresponding angles in parallel lines are always equal.
The information that [tex]L_2[/tex] makes a 20-degree angle seems to be incorrect if the lines [tex]L_1[/tex] and [tex]L_2[/tex] are truly parallel. It could be a typo or incorrect information since corresponding angles between [tex]L_1[/tex] and [tex]L_2[/tex] cannot differ if they are parallel.

In summary, given parallel lines and a transversal, corresponding angles should be equal. Therefore, [tex]L_1[/tex]'s angle with the transversal cannot be 30 degrees while [tex]L_2[/tex]'s angle with the transversal is 20 degrees, as that would contradict the rules of geometry regarding parallel lines.