Question

is △mnl ≅ △qnl? why or why not? no, there are no congruent sides. yes, they are congruent by either asa or aas. yes, they are both right triangles. no, ∠m is not congruent to ∠nlq.

Explanation:

Step1: Find angles in triangles

In $\triangle MNL$, $\angle MLN=32^{\circ}$, $\angle NML = 58^{\circ}$, so $\angle MNL=90^{\circ}$. In $\triangle QNL$, $\angle QLN = 32^{\circ}$, $\angle NQL=58^{\circ}$, $\angle QNL = 90^{\circ}$. Also, $LN$ is common to both triangles.

Step2: Apply congruence criteria

We have $\angle MLN=\angle QLN = 32^{\circ}$, $LN = LN$ (common side), and $\angle MNL=\angle QNL=90^{\circ}$ (ASA - Angle - Side - Angle). Or we can consider $\angle NML=\angle NQL = 58^{\circ}$, $\angle MLN=\angle QLN=32^{\circ}$, $LN=LN$ (AAS - Angle - Angle - Side).

Answer:

Yes, they are congruent by either ASA or AAS.