https://file.aiquickdraw.com/mathbot/file/1727372879933fpqrnh89.jpg

Let's analyze the problems in the image one by one.

### Problem 7: Find AB
- The total length of the line \(AC = 74\).
- The length of \(BC = 57\).
- We need to find \(AB\).

Using the relation:

\[
AB + BC = AC
\]

Substitute the known values:

\[
AB + 57 = 74
\]

Solving for \(AB\):

\[
AB = 74 - 57 = 17
\]

So, \(AB = 17\).

### Problem 8: Find UV
- The total length of the line \(TV = 78\).
- The length of \(TU = 68\).
- We need to find \(UV\).

Using the relation:

\[
TU + UV = TV
\]

Substitute the known values:

\[
68 + UV = 78
\]

Solving for \(UV\):

\[
UV = 78 - 68 = 10
\]

So, \(UV = 10\).

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Do you need any further details or have any other questions?

Here are some related questions for practice:
1. If \(AC = 90\) and \(BC = 40\), what is \(AB\)?
2. If \(TU = 55\) and \(TV = 90\), what is \(UV\)?
3. If \(AC = 100\) and \(AB = 30\), what is \(BC\)?
4. What would \(UV\) be if \(TV = 100\) and \(TU = 75\)?
5. How would you solve if both segments \(AB\) and \(UV\) were unknown?

**Tip:** Always subtract the known segment from the total to find the unknown segment in a line segment equation.

Find AB and UV based on the given line segments.

This problem involves finding unknown line segments AB and UV using the segment addition postulate. The total length of AC is 74 with BC given as 57, while TV is 78 with TU as 68. Learn the step-by-step approach to solve for the missing segments.

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