Question

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

Solution

## 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°.MathematicsRD Sharma (2019)All

Suggest Corrections

0

Similar questions
View More

Same exercise questions
View More

People also searched for
View More