Question

f $m\angle mnl =$ k $m\angle m =$

Explanation:

Step1: Find \(m\angle MNL\)

Vertical angles are equal. The angle adjacent to \(37^{\circ}\) and \(\angle MNL\) form a linear - pair. So \(m\angle MNL=180^{\circ}- 37^{\circ}=143^{\circ}\)

Step2: Find \(m\angle M\)

In right - triangle \(MLN\), the sum of angles is \(180^{\circ}\). We know \(\angle L = 90^{\circ}\) and from step1, the non - adjacent angle to \(\angle M\) (the angle at \(N\) inside the triangle) is \(180^{\circ}-143^{\circ}=37^{\circ}\). Using the angle - sum property of a triangle \(\angle M+\angle L+\angle N = 180^{\circ}\). Substitute \(\angle L = 90^{\circ}\) and \(\angle N=37^{\circ}\). Then \(\angle M=180^{\circ}-(90^{\circ}+37^{\circ})=53^{\circ}\)

Answer:

F. \(m\angle MNL = 143^{\circ}\)
K. \(m\angle M=53^{\circ}\)