In the given figure, O is the centre of a circle, ∠ ACB = 40°. Find ∠ OAB.

Question

Philoid · Accepted Answer

Given: ∠ACB = 40°

We know that ,

∠ AOB = 2×∠ACB

∠ AOB = 2×40 = 80°

∴ ∠AOB = 80°

In ΔAOB

OA = OB (radius)

∠OAB = ∠OBA (angles opposite to equal sides are equal)

Let ∠OAB = ∠OBA = x

By angle sum property

∠AOB + ∠OAB + ∠OBA = 180°

80 + x + x = 180°

80 + 2x = 180°

2x = 180° – 80° = 100°

x = = 50°

∴

In the given figure, O is the centre of a circle, ∠ACB = 40°. Find ∠OAB.