In figure, if ∠OAB = 40°, then ∠ACB is equal to—

Given ∠OAB = 40°

Consider ΔOAB,

⇒ OA = OB [radii of same circle]

We know that angles opposite to equal sides are equal.

⇒∠OBA = ∠OAB = 40°

By angle sum property,

⇒∠AOB + ∠OBA + ∠BAO = 180°

⇒∠AOB + 40° + 40° = 180°

⇒∠AOB = 180° - 80°

∴ ∠AOB = 100°

We know that the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.

⇒∠AOB = 2 ∠ACB

⇒ 100° = 2 ∠ACB

⇒∠ACB = 100°/ 2

∴ ∠ACB = 50°