Look at this diagram:STUVWXYZIf TV and WY are parallel lines and mTUS= 63°, what is mTUX?°

1. Break Down the Problem

We need to find the measure of angle $mTUX$ given that $TV$ and $WY$ are parallel lines, and the measure of angle $mTUS = 63^\circ$.

2. Relevant Concepts

Since $TV$ and $WY$ are parallel, we can use the properties of corresponding angles and alternate interior angles formed by a transversal. In this case, $TU$ acts as the transversal.

3. Analysis and Detail

1. Since $TV$ is parallel to $WY$, the angles formed by the transversal $TU$ will create corresponding angles.
2. The angle $mTUS$ (which is $63^\circ$) and $mTUX$ are alternate interior angles.
3. Thus, we have

$mTUX = mTUS$

4. Verify and Summarize

Since $mTUS = 63^\circ$:

$mTUX = 63^\circ$

Final Answer

The measure of angle $mTUX$ is $63^\circ$.