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To solve for \( x \) in the given problem involving parallelogram \( STUV \), here’s the breakdown of the steps:

### Information from the Problem:
1. \( SW = 52 \)  
2. \( WU = x - 3 \)  
3. \( WU \) and \( SW \) are given as segments of the diagonals of the parallelogram.

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### Key Property of Parallelogram Diagonals:
In a parallelogram, the diagonals **bisect each other**. This means that the point \( W \), where diagonals intersect, divides each diagonal into two equal parts.

So:  
- \( SW = WU + WS \), where \( WU \) and \( WS \) are equal halves of the diagonal \( SU \).

Thus, we write:
\[
WU = WS = \frac{SW}{2}
\]

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### Step-by-Step Solution:
1. \( SW = 52 \) (given). Since the diagonals are bisected:
   \[
   WU = WS = \frac{52}{2} = 26
   \]

2. \( WU \) is also given as \( x - 3 \). Therefore:
   \[
   x - 3 = 26
   \]

3. Solve for \( x \):
   \[
   x = 26 + 3
   \]
   \[
   x = 29
   \]

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### Final Answer:
The value of \( x \) is **29**.

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Let me know if you need a more detailed explanation or additional clarification!

### Related Questions:
1. What are the properties of diagonals in parallelograms?
2. How do you calculate segment lengths when diagonals bisect each other?
3. What is the difference between parallelogram and rhombus diagonals?
4. How do you prove that diagonals of a parallelogram bisect each other?
5. How can you find unknown variables in geometric diagrams involving midpoints?

### Tip:
In a parallelogram, the diagonals **always bisect each other** into equal halves—this property is key to solving many geometry problems.

Given parallelogram STUV below, SW = 52. If WU = x - 3, solve for x.

Learn how to solve for x in a parallelogram STUV where SW = 52 and WU = x - 3. Understand the property that diagonals of a parallelogram bisect each other, and solve step-by-step for the unknown variable. Suitable for Grades 8-10 geometry learners.

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