How can you tell which Angles are congruent from ADEF = AZXY?

  corresponding angles are listed in the same order

Step-by-step explanation:

Corresponding angles are listed in the same order in the triangle names. Corresponding angles are congruent.

  ∠D ≅ ∠Z

  ∠E ≅ ∠X

  ∠F ≅ ∠Y

This is why you have to carefully choose the names of triangles that you say are congruent. The sequence of the letters in the name carries significant information.