To solve this problem, let's analyze the given information and the diagram:

Given:

1. $\overline{RT} \parallel \overline{UW}$, which means these two lines are parallel.
2. $m\angle UVX = 42^\circ$.
3. We need to find $m\angle UVS$.

Solution:

In the diagram, $\overline{VX}$ acts as a transversal line intersecting the parallel lines $\overline{RT}$ and $\overline{UW}$.

Since $\overline{RT} \parallel \overline{UW}$:

• $\angle UVX$ and $\angle UVS$ are corresponding angles.

For parallel lines, corresponding angles are equal. Therefore: $m\angle UVS = m\angle UVX = 42^\circ$

Thus: $m\angle UVS = 42^\circ$

Would you like a deeper explanation or have any other questions?

Related Questions:

1. What are the properties of corresponding angles when lines are parallel?
2. How do alternate interior angles relate to parallel lines?
3. What is the sum of the interior angles formed by a transversal intersecting two parallel lines?
4. How can you identify parallel lines using transversal angles?
5. What is the difference between corresponding angles and alternate exterior angles?

Tip:

When dealing with parallel lines and transversals, always look for corresponding, alternate interior, and alternate exterior angles, as they help to quickly identify equal angle measures.