Question

use the diagram below to answer questions 1 and 2. 1. if lm = 22 and mn = 15, find ln. 2. if ln = 54 and lm = 31, find mn.

Explanation:

Step1: Understand segment - addition postulate

On a line segment \(LN\) with a point \(M\) between \(L\) and \(N\), \(LN=LM + MN\).

Step2: Solve for \(LN\) in question 1

Given \(LM = 22\) and \(MN=15\), substitute into the formula \(LN=LM + MN\).
\(LN=22 + 15\)
\(LN = 37\)

Step3: Solve for \(MN\) in question 2

Given \(LN = 54\) and \(LM = 31\), use the formula \(LN=LM + MN\), then \(MN=LN - LM\).
\(MN=54 - 31\)
\(MN = 23\)

Answer:

1. \(LN = 37\)
2. \(MN = 23\)