In the picture below, line PQ is parallel to line RS, and the lines are cut by a transversal, line TO. The transversal is not perpendicular to the parallel lines.

In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Congruent angles = ?
Step 02:
We must analyze the diagram to find the solution.
Congruent angles:
∠ Y ≅ ∠ E
The answer is:
∠ Y ≅ ∠ E : are congruent