In the given figure, O is the centre of the circle. If ∠OAB = 35° and C is a point on the circle, then ∠ACB = ?

1. 35°

2. 55°

3. 45°

4. 75°

Given,

Since O is the centre of the circle, OA and OB are both radii. OA = OB Therefore,

∠OBA = ∠OAB = 35° [Angles opposite to equal sides of a triangle are equal]

In ΔAOB,

By angle sum property of triangle,

∠OBA + ∠OAB + ∠AOB = 180°

35° + 35° + ∠AOB = 180°

∠AOB = 180° - 35° - 35°

∠AOB = 110°.

We know that,

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

⇒ ∠AOB = 2∠ACB

⇒ 110° = 2∠ACB

⇒ ∠ACB = $\dfrac{110^{\circ}}{2}$

⇒ ∠ACB = 55°.

Hence, option 2 is the correct option.