Analysis: Let ∠△DCE=x and ∠ACD=y, then ∠ACE=x+y, ∠ BCE = 90-∠ ACE = 90-X-Y, and get ∠ ACE = ∠ according to the equilateral corners.

Answer:

Solution: Let ∠DCE=x and ∠ACD=y, then ∠ACE=x+y, ∠ BCE = 90-∠ ACE = 90-X-Y. 。

AE = AC，

∴∠ACE=∠AEC=x+y，

BD = BC，

∴∠bdc=∠bcd=∠bce+∠dce=90-x-y+x = 90-y

In △DCE, ∫∠DCE+∠CDE+∠DEC = 180.

∴x+(90 -y)+(x+y)= 180，

X = 45，

∴∠DCE=45。

So the answer is: 45.