In the given figure, O is the centre of a circle and ∠OAB = 50°. Then, ∠CDA = ?

Question

In the given figure, O is the centre of a circle and ∠ OAB = 50°. Then, ∠ CDA = ?

Philoid · Accepted Answer

Given: ∠OAB = 50°

Construction: Join AC

Here,

In ΔAOB

OA = OB (radius)

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

∴ ∠OBA = 50°

∠OBA = ∠CDA (angles in the same segment)

∴ ∠CDA = 50°