Question

Is triangle MNL congruent to triangle QNL? Why or why not? Yes, they are congruent by either ASA or AAS. Yes, they are both right triangles. No, angle M is not congruent to angle NLQ. No, there are no congruent sides.

Answer 1

Its A

Explanation:

It is

Answer 2

See the attached figure which represent the rest of the question.
The rest of the question is the attached figure.
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As shown in the attached figure:
(1) ΔMNL is a right triangle at ∠MNL and ∠NML = 58°
∴ ∠L = 180° - (90°+58°) = 32°

(2) ΔQNL is a right triangle at ∠QNL and ∠QLN = 32°
∴ ∠Q = 180° - (90°+32°) = 58°

So, for both of ΔMNL and ΔQNL
1. ∠NLM = ∠ NLQ = 32°
2. ∠Q = ∠M = 58°
3. side NL = side NL
∴ ΔMNL is congruent to ΔQNL by AAS

=======OR=======

So, for both of ΔMNL and ΔQNL
1. ∠MNL = ∠QNL = 90°
2. side NL = side NL
3. ∠NLM = ∠ NLQ = 32°
∴ ΔMNL is congruent to ΔQNL by ASA

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So, the correct answer is the first option

Yes, they are congruent by either ASA or AAS