The correct answer for this question is this one:
we are given the statement that is
△ABC△ABC is similar to △LMN△LMN by the AA Similarity PostulateAA Similarity Postulate .
So, This means that angle A = Angle C
Angle C = 2(Angle M)
111 = 2 ( Angle M )
Angle M = 55.5 degrees
So, the correct answer for this question is 55.5 degrees