Question

11. In the given figure, O is the centre of the circle. Find angle AOC
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Answer 1

n △ABO, AO=BO⇒∠BAO=∠ABO=30o

In △CBO, CO=BO,⇒∠BCO=∠CBO=40o

⇒∠ABC=∠ABO+∠CBO=30+40=70o

Angle subtended at the center is twice the angle subtended anywhere on the arc, so,

∠AOC=2×∠ABC=140o

Answer 2

Step-by-step explanation:

Construction: Join BO

In ΔBOA, BO = AO [radii]

Thus, ∠A = ∠ABO = 30°

Similarly, ∠C = ∠CBO = 40°

Thus, ∠ABC = 70°

By the property that an arc subtend at the center an angle double of what it subtend at the circumference

Thus, ∠AOC = 2∠ABC = 2*70° = 140°

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