In the given image, we are provided with a diagram showing two parallel lines $\overleftrightarrow{SU}$ and $\overleftrightarrow{VX}$, and transversal lines cutting through them. We are also told that $\angle STW = 48.2^\circ$, and we need to find $\angle XWT$.

Key Information:

• $\overleftrightarrow{SU} \parallel \overleftrightarrow{VX}$ (parallel lines)
• $\angle STW = 48.2^\circ$ (given angle)
• We need to find $\angle XWT$.

Step-by-step explanation:

Since the lines $\overleftrightarrow{SU}$ and $\overleftrightarrow{VX}$ are parallel, the angles formed by the transversal follow properties of corresponding, alternate interior, or co-interior angles.

1. $\angle STW$ and $\angle XWT$ are alternate interior angles because they lie between the two parallel lines ($\overleftrightarrow{SU}$ and $\overleftrightarrow{VX}$) and on opposite sides of the transversal line $\overleftrightarrow{WT}$.

   By the Alternate Interior Angle Theorem, alternate interior angles are congruent when two lines are parallel.

Thus: $\angle XWT = \angle STW = 48.2^\circ$

Final Answer:

$\boxed{48.2^\circ}$

Would you like further details or have any questions about this solution? Here are some related questions to extend this concept:

1. What is the relationship between corresponding angles in parallel lines?
2. How can you use the Co-Interior Angle Theorem to solve similar problems?
3. What is the difference between alternate interior and alternate exterior angles?
4. How can you prove that two lines are parallel using angle relationships?
5. How does the transversal line affect the angles formed with parallel lines?

Tip: When working with parallel lines and transversals, remember that alternate interior, corresponding, and co-interior angles have specific relationships that help in solving for unknown angles.