△ABC is similar to △LMN by the AA Similarity Postulate . The measure of ∠A is 111º and m∠C=2(m∠M).
Since the Angle of A is 111 degrees.
Another angle, Angle of C is twice the angle of M.
Angle of A = Angle of C
2 (Angle of M) = Angle of C
2 (Angle of M) = 111
Angle of M = 55.5 degrees
