Circle has been constructed using chord AB subtending an angle of $75^{\circ}$ . Value of $∠ O A B$ is
15

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Solution

The correct option is A 15
In the figure, $∠ A C B = 75^{\circ} .$

So, $∠ A O B = 2 ∠ A C B ∠ A O B = 2 \times 75^{\circ} ∠ A O B = 150^{\circ}$

In $△ O A B$ , $O A = O B$ . [ $∵$ Radius of same circle].
So, $∠ O A B = ∠ O B A$ [ $∵$ Angles opposite to equal sides of an isosceles triangle are equal].

Now, $∠ A O B + ∠ O A B + ∠ O B A = 180^{\circ} 150^{\circ} + 2 ∠ O A B = 180^{\circ} 2 ∠ O A B = 180^{\circ} - 150^{\circ} 2 ∠ O A B = 30^{\circ} ∠ O A B = \frac{30^{\circ}}{2} ∠ O A B = 15^{\circ}$

Hence, the value of $∠ O A B$ in degrees is 15.

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Circle has been constructed using chord AB subtending an angle of 75∘. Value of ∠OAB is 15

Circle has been constructed using chord AB subtending an angle of $75^{\circ}$ . Value of $∠ O A B$ is
15