Question

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

Explanation:

Step1: Calculate ∠C in △ABC

The sum of angles in a triangle is $180^\circ$.
$\angle C = 180^\circ - 42^\circ - 65^\circ = 73^\circ$

Step2: Calculate ∠M in △MRQ

The sum of angles in a triangle is $180^\circ$.
$\angle M = 180^\circ - 42^\circ - 65^\circ = 73^\circ$

Step3: Match congruent parts

In △ABC and △MRQ:
$\angle A = \angle R = 42^\circ$, $\angle B = \angle Q = 65^\circ$, $\angle C = \angle M = 73^\circ$. The side between the two known angles (the included side) or non-included sides correspond, so ASA or AAS applies.

Answer:

Yes, they are congruent by either ASA or AAS.