Final answer:
The measure of angle DCE is 90 degrees.
Step-by-step explanation:
To find m <DCE, we need to use the fact that the angles in a triangle add up to 180 degrees.
Since m <DCF is 90 degrees, this means that DCF is a right angle. Therefore, the sum of m <DCF and m <DCE must be 180 degrees.
So, m <DCE = 180 - 90 = 90 degrees.