Question

Are the triangles congruent? Why or why not?

Answer 1

The correct answer is:

Yes, they are congruent by either ASA or AAS. 

We know one side is congruent with the marking, and two angles are at least congruent. 

I hope this helps!
~kaikers

Answer 2

Triangle ABC
unknown angle = 180 - 42 - 53 = 85
so measure of angles in triangle ABC: 42, 53, 85

triangle RMQ
unknown angle = 180 - 42 - 85 = 53
so measure of angles in triangle RMQ: 42, 53, 85

both triangles are congruent

answer
Yes, all the angles of each of the triangles are acute.