To solve the problem, we first note that if the sides of triangles \(\Delta ABC\) and \(\Delta DEF\) are parallel, then this indicates that the two triangles are similar due to the properties of parallel lines and transversals.
The problem states that the complement of angle \(A\) is \(65^\circ\). This means:
\[ \text{Angle } A + 65^\circ = 90^\circ \]
From this equation, we can find angle \(A\):
\[ \text{Angle } A = 90^\circ - 65^\circ = 25^\circ \]
Since \(\Delta ABC\) and \(\Delta DEF\) are similar due to the parallel sides, the corresponding angles are equal. Therefore, if angle \(A\) in triangle \(ABC\) corresponds to angle \(D\) in triangle \(DEF\), we have:
\[ \text{Angle } D = \text{Angle } A = 25^\circ \]
Thus, the measure of angle \(D\) is:
\[ \boxed{25^\circ} \]