Question

the figure shows three lines that intersect at point n. angle gnh is congruent to angle knl. angle mnl is complementary to angle knl. what is the measure of angle mnl? 42° 48° 132° 138°

Explanation:

Step1: Find the measure of \(\angle KNL\)

Since \(\angle GNH\) and \(\angle KNL\) are congruent (given), and \(\angle GNH = 42^{\circ}\) (from the figure), so \(\angle KNL=42^{\circ}\).

Step2: Use the definition of complementary angles

Complementary angles sum to \(90^{\circ}\). Let \(x = \angle MNL\). We know \(x+\angle KNL = 90^{\circ}\). Substitute \(\angle KNL = 42^{\circ}\) into the equation: \(x+42^{\circ}=90^{\circ}\).

Step3: Solve for \(x\)

Subtract \(42^{\circ}\) from both sides: \(x=90^{\circ}- 42^{\circ}=48^{\circ}\). So \(\angle MNL = 48^{\circ}\).

Answer:

B. \(48^{\circ}\)