To solve this problem, we will use the Segment Addition Postulate, which states that the sum of the lengths of the smaller segments will equal the total length of the larger segment.

Given:

1. $ST = 13$
2. $TU = 6$
3. $UV = 2x - 18$
4. The total length $SV = 4x - 29$

According to the Segment Addition Postulate: $ST + TU + UV = SV$

Substitute the given values: $13 + 6 + (2x - 18) = 4x - 29$

Let's simplify and solve for $x$:

1. Combine like terms on the left side: $19 + 2x - 18 = 4x - 29$

2. Simplify further: $1 + 2x = 4x - 29$

3. Subtract $2x$ from both sides: $1 = 2x - 29$

4. Add 29 to both sides: $30 = 2x$

5. Divide by 2: $x = 15$

So, the measure of $x$ is 15.

Would you like me to go into further detail or do you have any specific questions?

Related Questions:

1. What is the length of segment $UV$ when $x = 15$?
2. What is the length of segment $SV$ using the value of $x$?
3. Can the Segment Addition Postulate be applied to other geometric figures?
4. How would the equation change if segment $TU$ had a different length?
5. What other geometric properties rely on the Segment Addition Postulate?

Tip:

When solving for variables, always check your solution by substituting the value back into the original equations to verify accuracy.