In the given figure, AB is the side of regular pentagon and BC is the side of regular hexagon. Angle BAC is :

1. 132°

2. 66°

3. 90°

4. 120°

Since,

AB is the side of regular pentagon.

∴ ∠AOB = $\dfrac{360°}{5}$ = 72°.

BC is the side of regular hexagon.

∴ ∠BOC = $\dfrac{360°}{6}$ = 60°.

From figure,

∠AOC = ∠AOB + ∠BOC = 72° + 60° = 132°.

We know that,

The angle which an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circumference.

⇒ ∠AOC = 2∠APC

⇒ ∠APC = $\dfrac{∠AOC}{2} = \dfrac{132°}{2}$ = 66°.

Hence, Option 2 is the correct option.