Question

these figures are congruent. what is st?
$square$ miles

Explanation:

Step1: Find missing angle in $\triangle LNM$

Sum of angles in a triangle is $180^\circ$.
$\angle M = 180^\circ - 59^\circ - 41^\circ = 80^\circ$

Step2: Match congruent triangle parts

In $\triangle LNM$ and $\triangle SUT$: $\angle N = \angle S = 59^\circ$, $\angle M = \angle T = 80^\circ$, side $LN = side SU = 74$ mi. So $\triangle LNM \cong \triangle SUT$ (AAS). Corresponding side $ST$ matches $NM$.

Step3: Identify length of $ST$

$NM = 50$ mi, so $ST = NM$.

Answer:

50 miles