Question

1. if $lm = 22$ and $mn = 15$, find $ln$.
2. if $ln = 54$ and $lm = 31$, find $mn$.

Explanation:

Step1: Use segment - addition postulate

If points $L$, $M$, and $N$ are collinear, then $LN=LM + MN$.

Step2: Solve for part 1

Given $LM = 22$ and $MN=15$, substitute into the formula: $LN=22 + 15$.
$LN=37$

Step3: Rearrange the formula for part 2

We know $LN=LM + MN$, so $MN=LN - LM$.

Step4: Solve for part 2

Given $LN = 54$ and $LM = 31$, substitute into the formula: $MN=54-31$.
$MN = 23$

Answer:

1. $LN = 37$
2. $MN=23$