In the right triangle ABD
Available < a = 90-50 = 40
AB = AC
∴∠ABC=∠ACB
That is ∠ ABC =∠ ACB = (180-40)/2 = 70.
Yes, there is another possibility.
AB=AC, BD is AC high, ∠DBA=50.
In the right triangle ABD
Available D = 90-50 = 40
∴∠BAC= 180-40= 140
AB = AC
∴∠ABC=∠ACB
That is ∠ ABC =∠ ACB = (180-140)/2 = 20.