Question

if angle oab =40°,then measure angle acb is​

Answer 1

Step-by-step explanation:

In ΔQAB, OA = OB [both are the radius of a circle]

∠OAB = ∠OBA ⇒ ∠OBA = 40°

[angles opposite to equal sides are equal] Also, ∠AOB + ∠OBA + ∠BAO = 180°

[by angle sum property of a triangle]

∠AOB + 40° + 40° = 180°

⇒ ∠AOB = 180° – 80° = 100°

We know that, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.

∠AOB = 2 ∠ACB ⇒ 100° =2 ∠ACB

∠ACB = 100°/2 = 50°