In the given figure, O is center of the circle and ∠B = 55°. The angle A is equal to :

1. 55°

2. 35°

3. 45°

4. 50°

From figure,

In △ OCB,

OB = OC (Radius of common circle)

We know that,

Angles opposite to equal sides of a triangle are equal.

∴ ∠C = ∠B = 55°

By angle sum property of triangle,

⇒ ∠C + ∠B + ∠O = 180°

⇒ 55° + 55° + ∠O = 180°

⇒ ∠O + 110° = 180°

⇒ ∠O = 180° - 110° = 70°.

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.

⇒ ∠O = 2∠A

⇒ ∠A = $\dfrac{∠O}{2} = \dfrac{70°}{2}$ = 35°.

Hence, Option 2 is the correct option.