Triangle abc is similar to triangle lmn by the aa similarity postulate.

also, m∠a = 144° and m∠c = 2(m∠m).

what is m∠m?

°

Well looking at the information in triangle ABC you know 

Angle B + Angle C = 180 - 144

so Angle B + Angle C = 36

since the triangles are similar let angle M = x   

then Angle C = 2x        and angle B = angle M but the similarity postulate

so form an equation 

2x + x = 36 

solve for x 

Hope it helps