Final answer:
The statement that is true when m∠E=m∠Y and m∠F=m∠X is that the angles are congruent; it does not imply similarity or congruency of triangles nor that the angles are supplementary.
Step-by-step explanation:
The angles are congruent. If m∠E = m∠Y and m∠F = m∠X, this implies that the measures of angle E and angle Y are equal, and the measures of angle F and angle X are equal. This characteristic of angles is known as congruency, which means that they have the exact same measure.
However, without additional information about the sides of the triangles, we cannot determine similarity or congruency of triangles. Angles being supplementary means that their measures add up to 180 degrees, which is not implied here. Thus, option C is not correct, and neither are options B and D regarding the similarity or congruency of triangles based solely on these angle relationships.
If m∠E=m∠Y and m∠F=m∠X, then it means that angles E and Y are congruent (equal) and angles F and X are also congruent (equal).
Therefore, the statement that is true in this case is option A) The angles are congruent.
Similar angles have the same measure, while congruent angles have the same measure and the same shape. In this case, we have congruent angles, which means they are equal in measure and shape.