In figure, ∠ACB = 40°. Find ∠OAB.

Given ∠ACB = 40°

We know that a segment subtends an angle to the circle is half the angle that subtends to the circle.

i.e. ∠AOB = 2 ∠ACB

⇒∠AOB = 2 (40°)

⇒∠AOB = 80° … (1)

In ΔAOB,

⇒ OA = OB [Radii of same circle]

We know that angles opposite to equal sides are equal.

∴ ∠OBA = ∠OAB

We know that sum of all angles in a triangle is 180°.

⇒∠AOB + ∠OBA + ∠OAB = 180°

⇒ 80° + ∠OAB + ∠OAB = 180°

⇒ 2∠OAB = 180° - 80°

⇒ 2∠OAB = 100°

⇒∠OAB = 100°/ 2

∴ ∠OAB = 50°