Question

PLEASE HELP. WILL GIVE BRAINLIEST

Answer 1

∠M corresponds to ∠B, so we have ...
  m∠C = 3(m∠B)

Then the sum of angles of the triangle is
  m∠A + m∠B + m∠C = 180°
  60 + B + 3B = 180 . . . . . . . . . use B to mean m∠B
  4B = 120
  B = 120/4 = 30

m∠M = m∠B = 30°

Answer 2

Triangle ABC is similar to triangle LMN
m<A = m<L = 60
m<C = m<N
m<B = m<M

Lets x = m<M
so 
m<C = m<N = 3x

and sum of interior angles of a triangle = 180
so
m<L + m<N + m<M = 180
60 + 3x + x + 180
4x + 60 = 180
4x = 120
  x = 30

m<M =  x = 30 

answer
m<M = 30°