Final answer:
Given that ∠ZDCB is a right angle and m ∠DCE is 39°, the measure of ∠BCE is found to be 51° by subtracting the known angles from 180°.
Step-by-step explanation:
If ZDCB is a right angle, that means ∠ZDCB measures 90°. Given that m ∠DCE is 39°, we can deduce the measure of ∠BCE by understanding that angles on a straight line sum to 180°. Since ∠ZDCB is a right angle, then the straight line is shared between ∠DCE and ∠BCE. The calculation to find the measure of ∠BCE becomes:
180° - 90° (right angle) - 39° (m ∠DCE) = 51°.
Therefore, the measure of ∠BCE is 51°.