Since ∆LMN is isosceles, we have m∠N = m∠L = 36 degrees. Also, m∠N + m∠M + m∠L = 180 degrees by the angle sum property of triangles. Substituting the given values, we have 36 + m∠M + 36 = 180. Simplifying, we get m∠M = 180 - 72 = 108 degrees. Therefore, the measures of angles M and N are 108 degrees and 36 degrees, respectively.
