In a rhombus, the diagonals bisect each other at right angles. Given that \( DE \) is perpendicular to \( AC \) and that \( mEDC = 42^\circ \), we can determine that the angles created by the diagonals will also reflect this relationship.
Since \( DE \) and \( AC \) bisect each other perpendicularly, angle \( EDC \) is equal to angle \( ECA \). Therefore, if \( mEDC = 42^\circ \), then \( mECD \) can be found using the fact that the angles around point D must sum up to \( 180^\circ \) due to the straight line defined by points E through D through C.
Thus,
\[ mECD + mEDC = 90^\circ \]
As it’s a right angle formed by the intersection of the diagonals, we can conclude:
\[ mECD = 90^\circ - mEDC = 90^\circ - 42^\circ = 48^\circ \]
So, the measurement of \( mECD \) is:
mECD is \( 48^\circ \).
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