Question

In the given figure, if ∠OAB = 40∘ , then ∠ACB = ____________

Answer 1

Given:
∠OAB = 40° ...(1)


In ∆OAB,
OA = OB
∴ ∠OAB = ∠OBA = 40° (angles opposite to equal sides are equal) ...(2)

Now,
∠OAB + ∠OBA + ∠AOB = 180° (angle sum property)
⇒ 40° + 40° + ∠AOB = 180° (From (1) and (2))
⇒ ∠AOB = 180° − 80°
⇒ ∠AOB = 100° ...(3)


We know, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.
Thus, ∠AOB = 2∠ACB
⇒ 100° = 2∠ACB (From (3))
⇒ ∠ACB = 50°


Hence, ∠ACB = 50°.