Question

if angle ABC =30 , the. find Angle AOC
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Answer 1

Answer:

∠AOC = 2 ∠ABC = 2 × 30° = 60°

Step-by-step explanation:

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Answer 2

Answer:

∠AOC = 2 ∠ABC = 2 × 30° = 60°

Explanation :- In △AOB

In △AOBOA=OB

In △AOBOA=OB∴∠OAB+∠OBA+∠AOB=180°

=>2∠OAB+90°=180°

=>2∠OAB=180°−90°

                         =90°

=>∠OAB=290°

                      =45°

We know that the angle inscribed at the centre of the circle by an arch is twice the angle subtended at the circumference by the same arch.

We know that the angle inscribed at the centre of the circle by an arch is twice the angle subtended at the circumference by the same arch.∴∠ACB=21∠AOB

We know that the angle inscribed at the centre of the circle by an arch is twice the angle subtended at the circumference by the same arch.∴∠ACB=21∠AOB                 =29°

                 =45°

Again in △ABC

Again in △ABC∠ACB+∠CBA+∠BAC=180°

=>45°+30°+∠BAC=180°

=>∠BAC=180°−75°

                      =105°

∴∠CAO=∠BAC−∠OAB

∴∠CAO=∠BAC−∠OAB=>∠CAO=105°−45°

                     =60°