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.