Question

if $angle 8 cong angle 10$ and $angle 1 cong angle 7$, which describes all the lines that must be parallel?
only lines $r$ and $s$ must be parallel.
only lines $t$ and $u$ must be parallel.
lines $r$ and $s$ and lines $t$ and $u$ must be parallel.
neither lines $r$ and $s$ nor lines $t$ and $u$ must be parallel.

Explanation:

Step1: Analyze $\angle8\cong\angle10$

$\angle8$ and $\angle10$ are alternate interior angles formed by transversal $s$ intersecting lines $t$ and $u$. By the converse of the alternate interior angles theorem, if alternate interior angles are congruent, the lines cut by the transversal are parallel. So $t \parallel u$.

Step2: Analyze $\angle1\cong\angle7$

$\angle1$ and $\angle7$ are alternate exterior angles formed by transversal $t$ intersecting lines $r$ and $s$. By the converse of the alternate exterior angles theorem, if alternate exterior angles are congruent, the lines cut by the transversal are parallel. So $r \parallel s$.

Answer:

Lines r and s and lines t and u must be parallel.