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The problem asks to find the measure of angle \( \angle S \) in parallelogram \( RSTU \), where the measure of \( \angle U \) is given as \( 2w - 51^\circ \).

### Key Properties of Parallelograms:
1. Opposite angles are equal.
2. Adjacent angles are supplementary, meaning they add up to \( 180^\circ \).

Since \( RSTU \) is a parallelogram:
- \( \angle S \) and \( \angle U \) are supplementary, so:
\[
\angle S + \angle U = 180^\circ
\]
- We are given \( \angle U = 2w - 51^\circ \), so:
\[
\angle S + (2w - 51^\circ) = 180^\circ
\]
Solve for \( \angle S \):
\[
\angle S = 180^\circ - (2w - 51^\circ)
\]
\[
\angle S = 180^\circ - 2w + 51^\circ
\]
\[
\angle S = 231^\circ - 2w
\]

Now, if the value of \( w \) is known, you can substitute it into this equation to get the specific measure of \( \angle S \). Do you have the value of \( w \) or would you like me to assist further with this?

Let me know if you'd like more details or have any other questions!

### Further Exploration:
1. What is the relationship between other angles in a parallelogram?
2. How can the properties of parallelograms help solve for unknown angles?
3. Can adjacent angles in a parallelogram ever be equal?
4. How does the formula for supplementary angles apply to parallelograms?
5. How would the solution change if \( w \) were explicitly given?

**Tip:** Always check if the angles given are adjacent or opposite to help determine the correct relationships in parallelograms!

Find the measure of angle S in parallelogram RSTU, where angle U is given as 2w - 51 degrees.

Solve for the measure of angle S in parallelogram RSTU, given that angle U is 2w - 51 degrees. Explore key geometric concepts related to the properties of parallelograms and supplementary angles. This problem is suitable for students in Grades 8-10.

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