In the given figure, O is the centre of the circle.
If ∠AOB = 110° and ∠AOC = 80°, then ∠BAC = ?

1. 75°

2. 80°

3. 85°

4. 95°

From figure,

∠BOC = 360° - (∠AOB + ∠AOC)

∠BOC = 360° - (110° + 80°)

= 360° - 190°

= 170°.

We know that,

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

∴ BOC = 2∠BAC

∴ ∠BAC = $\dfrac{1}{2}$ ∠BOC

= $\dfrac{170^{\circ}}{2}$ = 85°.

Hence, option 3 is the correct option.