In the adjoining figure, AB = AC and BD = CD. Then, ∠ADC =

1. 60°

2. 75°

3. 90°

4. 100°

In △ABD and △ACD,

⇒ AD = AD (Common side)

⇒ BD = CD (Given)

⇒ AB = AC (Given)

∴ △ABD ≅ △ACD (By S.S.S axiom)

⇒ ∠ADB = ∠ADC = x (let) (Corresponding parts of congruent triangles are equal)

From figure,

⇒ ∠ADB + ∠ADC = 180° (Linear pair)

⇒ x + x = 180°

⇒ 2x = 180°

⇒ x = $\dfrac{180°}{2}$

⇒ x = 90°

⇒ ∠ADB = ∠ADC = 90°.

Hence, option 3 is the correct option.