The question asks for $m \angle TUR$, given that $QS$ and $TV$ are parallel lines and $m \angle VUW = 121^\circ$.

Steps to solve:

1. Identify the transversal: Line $WU$ acts as a transversal intersecting the parallel lines $QS$ and $TV$.

2. Use the Alternate Interior Angle Theorem: Since $QS \parallel TV$ and $WU$ is a transversal, alternate interior angles formed by the transversal with the parallel lines are equal.

   So, $\angle TUR$ is an alternate interior angle to $\angle VUW$, meaning: $m \angle TUR = m \angle VUW = 121^\circ$

Thus, the measure of $\angle TUR$ is 121°.

Would you like more details or have any other questions?

Here are 5 related questions to consider:

1. How are alternate interior angles defined for parallel lines?
2. What are the properties of corresponding angles with a transversal?
3. What is the relationship between consecutive interior angles and parallel lines?
4. How can the same properties be applied if the transversal intersects at different angles?
5. Can you prove why two alternate interior angles are congruent using geometry postulates?

Tip: Always remember, when two parallel lines are cut by a transversal, the alternate interior angles are congruent!