Question

in a circle with center o it angle AOB = 90 degree angle ABC = 30 degree angle AOB is the center angle ACB is the inscribed angle . find angle CAO ​

Answer 1

Answer:

Step-by-step explanation:

0∠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°