Question

In the given figure, O is the centre of the circle and angle OAB = 55°, then angle ACB is equal to:

Options

• 55°

• 35°

• 70°

• 30°

Answer 1

35°

Explanation:

From figure,

In △OAB,

OA = OB (Radius of same circle)

We know that,

Angles opposite to equal sides are equal.

∴ ∠OBA = ∠OAB = 55°

By angle sum property of triangle,

⇒ ∠OBA + ∠OAB + ∠AOB = 180°

⇒ 55° + 55° + ∠AOB = 180°

⇒ ∠AOB + 110° = 180°

⇒ ∠AOB = 180° − 110° = 70°

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.

∴ ∠AOB = 2∠ACB

∠ACB = `(∠AOB)/2 = (70°)/2`​ = 35°