Question

10 fill in the blank 1 point 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: Use segment - addition postulate

Since $LN=LM + MN$ for collinear points $L$, $M$, and $N$.

Step2: Solve for $LN$ in the first case

Given $LM = 22$ and $MN=15$, then $LN=22 + 15$.
$LN=37$

Step3: Solve for $MN$ in the second case

Using $LN=LM + MN$, we can rewrite it as $MN=LN - LM$. Given $LN = 54$ and $LM = 31$, then $MN=54-31$.
$MN = 23$

Answer:

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