There isn't enough information in the question. The only possible answer is that

∠BAD = 180° - any one of the blue shaded angle or
∠BAD = 90° + ∠ACB


Unless, △ACD is an equilateral △.
Then ∠ACD = ∠ADC = ∠CAD = ∠BAC = 60°

Which ∠BAD = 180° - 60° = 120°

Check with the teacher to see if it should be an equilateral △ instead of an isosceles △

Have seen your suggested solution. But there's one problem. Are you very certain that AC is the angle bisector of ∠ BAE?

You're right. It's an assumption made based on the limited information of the question.

If that's the case then ABCE would be a square instead of a rectangle as you mentioned. And if that's the case, you would end up getting ∠DAC = 90°, which doesn't match the acute angle shown in the drawing

True