Question

these figures are congruent. what is rs?
miles

Explanation:

Step1: Match congruent triangle parts

In $\triangle LNM$ and $\triangle RTS$, $\angle L = \angle T = 62^\circ$, $LM = TS = 55$ mi, $LN = TR = 37$ mi. So $\triangle LNM \cong \triangle RTS$ by SAS congruence.

Step2: Identify corresponding side of RS

The side corresponding to $RS$ is $NM$.

Step3: Assign length to RS

Length of $NM = 50$ mi, so $RS = NM$.

Answer:

50 miles