∠∠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 ~)