In the given figure, O is a centre of a circle. If ∠OAB = 40° and C is a point on the circle, then ∠ACB = ?
In Δ AOB OA = OB( radius)
OAB = OBA (Angles opposite to equal sides are equal)
OBA = 40
By angle sum property
OAB + OBA + AOB = 180°
AOB = 180° – OAB – OBA
AOB = 180° – 40° – 40° = 100°
We know that
2 ×ACB = AOB (The angle subtended by an arc at the center is twice the angle subtended by the same arc on any point on the remaining part of the circle).
2 ×ACB = 100°
ACB = 50
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