#### Question

In the given figure, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°; Find:

(i) ∠ACB, (ii) ∠OBC, (iii) ∠OAB, (iv) ∠CBA.

#### Solution

Here,` ∠ACB = 1/2`Reflex (∠AOB) =`1/2 (360° -140°) = 110°`

(Angle at the centre is double the angle at the circumference subtended by the same chord)

Now, OA = OB (Radii of same circle)

∴ ∠OBA = ∠OAB = `(180° -140°)/2`= 20°

∴ ∠CAB = 50° - 20°= 30°

ΔCAB,

∠CBA - 180° -110°- 30° = 40°

∴ ∠OBC = ∠CBA + ∠OBA = 40° + 20° = 60°

Is there an error in this question or solution?

Solution In the Given Figure, O is the Centre of the Circle. If ∠Aob = 140° and ∠Oac = 50°; Find: (I) ∠Acb, (Ii) ∠Obc, (Iii) ∠Oab, (Iv) ∠Cba. Concept: Concept of Circles.