∠∠BHD =∠AHE, and ∠∠ AEH =∠ ADC = 90,

∴∠DAC+∠C=90，∠HAE+∠AHE=90，

∴∠AHE=∠C，

∴∠C=∠BHD，

BH = AC，∠HBD=∠DAC，∠C=∠BHD，

∴△HBD≌△CAD，

∴AD=BD.

As shown in figure (1) ∠ ABC = 45;

As shown in figure (2), ∠ ABC = 135.

∵AD=BD,AD⊥BD，

△ ADB is an isosceles right triangle,

∴∠ABD=45，

∴∠ABC= 180 -45 = 135，

So the answer is: when H is inside △ABC 45 or when H is outside △ABC 135.

(Because pictures can't be uploaded, you can draw them yourself ~)