Let's analyze and solve each of the three problems presented in the image:

Problem 10: Find $EG$

We are given the following distances on the segment $EG$:

• $EF = 22$
• $FG = 93$

To find the length of $EG$, we add the given distances: $EG = EF + FG = 22 + 93 = 115$

Answer: $EG = 115$

Problem 11: Find $JL$

We are given the following distances on the segment $JL$:

• $JK = 15$
• $KL = 67$

To find the length of $JL$, we add the given distances: $JL = JK + KL = 15 + 67 = 82$

Answer: $JL = 82$

Problem 12: Find $FG$

We are given the following distances on the segment $FH$:

• $FG$ is unknown.
• $GH = 22$
• $FH = 61$

Since $FH$ is the total length and $FG + GH = FH$, we can solve for $FG$ as follows: $FG = FH - GH = 61 - 22 = 39$

Answer: $FG = 39$

Summary of Answers:

• $EG = 115$
• $JL = 82$
• $FG = 39$

Would you like any further explanations or details?

Here are 5 related questions to expand your understanding:

1. If $EG$ is 115 and we move 25 units from point $E$, where would we be on the line?
2. How would you find the missing segment if only the total length and one segment are known?
3. How could you use similar methods to solve for unknowns on a triangle or polygon?
4. What is the general formula for finding a total length from two segments on a line?
5. How can you check your answers to problems like these?

Tip: When dealing with segment addition problems, always confirm the units and ensure all parts of the segment sum to the total.