In the given figure,O is the centre of circle, if angle OAB = 30 and angle OCB = 40, then - Maths - Circles

Question

In the given figure,O is the centre of circle, if angle OAB = 30
and angle OCB = 40, then find measure of angle AOC ?​

Varun.Rawat · Accepted Answer

We have :OA = OB = OC  radii of same circleIn ∆OAB,     OB = OA⇒∠OAB = ∠OBA  Angles opposite to equal sides are equal⇒∠OAB = 30°In ∆OAC,     OC = OA⇒∠OAC = ∠OCA  Angles opposite to equal sides are equal⇒∠OAC = 40°Now, ∠BAC = ∠OAB + ∠OAC = 30°+40° = 70°Now, we know that angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle
Now, ∠BOC = 2∠BAC = 2×70° = 140°

In the given figure,O is the centre of circle, if angle OAB = 30 and angle OCB = 40, then find measure of angle AOC ?​

In the given figure,O is the centre of circle, if angle OAB = 30 and angle OCB = 40, then find measure of angle AOC ?