the figure shows three lines that intersect at point n. angle gnh is congruent to angle knl. angle mnl is…

Explanation:

Step1: Identify congruent angles

Since $\angle GNH$ and $\angle KNL$ are congruent, and $\angle GNH = 48^{\circ}$, then $\angle KNL=48^{\circ}$.

Step2: Use the complementary - angle relationship

Complementary angles add up to $90^{\circ}$. Let $\angle MNL = x$. Since $\angle MNL$ is complementary to $\angle KNL$, we have $x+\angle KNL = 90^{\circ}$. Substitute $\angle KNL = 48^{\circ}$ into the equation: $x+48^{\circ}=90^{\circ}$.

Step3: Solve for the angle measure

Subtract $48^{\circ}$ from both sides of the equation: $x=90^{\circ}-48^{\circ}=42^{\circ}$.

Answer:

$42^{\circ}$