( 1)、AB=AC、AD=AE、∠BAD=∠BAC-∠DAC=∠DAE-∠DAC=∠CAE

So: triangle BAD is congruent with triangle CAE, so ∠B=∠ACE.

(2) From (1), it is known that ∠ ace = ∠ b = 45,

(a): ef = EC, then: ∠ EFC = 45 = ∠ CAE+∠ AEF = 45+∠ CAE. Get ∠ CAE = 0, when C and E coincide, D and B coincide, ∠ Bad = 0, which is irrelevant at this time.

(b): CE = CF，∠ CFE = 67.5 = ∠ CAE+∠ AEF = 45+∠ CAE，∠ CAE = 12.5，∠ Bad = 65438。

(c): cf = ef，∠ cfe = 90 = ∠ CAE+∠ AEF = 45+∠ CAE，∠ CAE = 45，∠ bad = 45。

To sum up: ∠ bad = 45 or 12.5.