Final answer:
The correct answer is LM = 7 and MN = 16.
Step-by-step explanation:
To solve for segments LM and MN, we need to add the lengths of the segments together. For option a) LM = 4 and MN = 36, we get a total length of 4 + 36 = 40. So, LM = 4 and MN = 36 is incorrect.
For option b) LM = 9 and MN = 18, we get a total length of 9 + 18 = 27. So, LM = 9 and MN = 18 is incorrect.
For option c) LM = 5 and MN = 50, we get a total length of 5 + 50 = 55. So, LM = 5 and MN = 50 is incorrect.
For option d) LM = 7 and MN = 16, we get a total length of 7 + 16 = 23. So, LM = 7 and MN = 16 is correct.