In the given figure, O is the center of a circle. AB is the side of a square and BC is side of a regular hexagon. Also arc AD = arc CD. Angle DOC is equal to :

1. 150°

2. 105°

3. 130°

4. 210°

Join OD.

Since, AB is the side of square.

∴ ∠AOB = $\dfrac{360°}{4}$ = 90°.

Since, BC is the side of regular hexagon.

∴ ∠BOC = $\dfrac{360°}{6}$ = 60°.

We know that,

Equal arcs subtends equal angles at the center.

Since, arc AD = arc CD

∴ ∠AOD = ∠COD = x (let)

From figure,

⇒ ∠AOD + ∠COD + ∠AOB + ∠BOC = 360°

⇒ x + x + 90° + 60° = 360°

⇒ 2x + 150° = 360°

⇒ 2x = 360° - 150°

⇒ 2x = 210°

⇒ x = $\dfrac{210°}{2}$ = 105°.

Hence, Option 2 is the correct option.