Question

In the given figure, O is centre of the circle and \[\angle \mathrm{B}=55^{\circ}\]. The angle A is equal to ______.

Options

• 55°

• 35°

• 45°

• 50°

Answer 1

In the given figure, O is centre of the circle and \[\angle \mathrm{B}=55^{\circ}\]. The angle A is equal to 35°.

Explanation: 

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 = `(∠O)/2 = (70°)/2`​ = 35°