Line segment WZ is shown below and where WX = 2x, XY = 3x + 1, YZ = 8, and WZ = 29. Match missing measures.

To solve for the missing measures on line segment \( WZ \), we use the information provided:

- \( WX = 2x \)
- \( XY = 3x + 1 \)
- \( YZ = 8 \)
- \( WZ = 29 \)

The total length of line segment \( WZ \) is the sum of \( WX \), \( XY \), and \( YZ \):
\[
WZ = WX + XY + YZ
\]
Substituting the given expressions into this equation:
\[
29 = (2x) + (3x + 1) + 8
\]
Now simplify and solve for \( x \):
\[
29 = 2x + 3x + 1 + 8
\]
\[
29 = 5x + 9
\]
Subtract 9 from both sides:
\[
20 = 5x
\]
Now divide by 5:
\[
x = 4
\]

### Step 2: Finding the missing measures
Now that we know \( x = 4 \), we can substitute it back into the expressions for \( WX \) and \( XY \):

- \( WX = 2x = 2(4) = 8 \)
- \( XY = 3x + 1 = 3(4) + 1 = 12 + 1 = 13 \)

So the missing measures are:
- \( WX = 8 \)
- \( XY = 13 \)
- \( YZ = 8 \) (already given)

### Summary of measures:
- \( WX = 8 \)
- \( XY = 13 \)
- \( YZ = 8 \)
- \( WZ = 29 \) (total length)

Would you like any further clarification or details?

Here are 5 follow-up questions to expand your understanding:
1. How can we verify the total length \( WZ \) from the segment measures?
2. What happens if we change the value of \( YZ \) while keeping \( WZ \) constant?
3. How would the expressions change if \( WZ \) were given as a variable instead of a number?
4. Can you find an alternate method to solve for \( x \) in this type of problem?
5. How would you solve for missing lengths if you were given angle measures instead?

**Tip:** When solving geometry problems, always remember that the sum of smaller segment lengths equals the total length of the larger segment.

In this problem, we solve for missing measures on line segment WZ, where WX = 2x, XY = 3x + 1, YZ = 8, and WZ = 29. Follow the step-by-step solution that uses algebra and the Segment Addition Postulate. Suitable for students in Grades 6-8.

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