Question

Triangle ABC is similar to triangle XYZ by the AA Similarity Postulate.

Answer 1

$m\angle Y=m\angle B\\\\ m\angle B=180-m\angle A-m\angle C\\ m\angle B=180-39-24\\ m\angle B=117^{\circ} \\ \Downarrow\\ \boxed{m\angle Y=117^{\circ}}$