For an isosceles triangle
∠ABC = ∠ACB = 35°
Let the ∠ADB be x
Then,
∠ADC = 180° - x
As AD is median so BD = CD
And for isosceles triangle AB = AC
So,
\(\frac{AB}{AC}\) = \(\frac{BD}{CD}\) = 1
By angle bisector theorem,
∠BAD = ∠CAD = y (Let)
For ΔBAD
35 + x + y =180 (i)
For ΔDAC
35 + 180 – x + y = 180 (ii)
35 + y = x
Therefore,
35 + 34 + y + y = 180°
2y + 70 = 180°
2y = 100°
y = 55°
Therefore,
∠BAD = ∠CAD = 55°