Question

are the triangles congruent? why or why not?
no, the congruent sides do not correspond.
no, ∠b is not congruent to ∠q.
yes, they are congruent by either asa or aas.
yes, all the angles of each of the triangles are acute.

Explanation:

Step1: Calculate angles in triangle \(ABC\)

Sum of angles in a triangle is \(180^{\circ}\). For \(\triangle ABC\), \(\angle C=180^{\circ}-42^{\circ}-53^{\circ}=85^{\circ}\)

Step2: Check congruence criteria

In \(\triangle ABC\) and \(\triangle RMQ\), \(\angle A = \angle R = 42^{\circ}\), \(AB = RM\) (marked equal), \(\angle C=\angle Q = 85^{\circ}\). By \(AAS\) (two angles and a non - included side), the triangles are congruent.

Answer:

Yes, they are congruent by either ASA or AAS.