Question

In the given figure, O is the centre of the circle. If $\angle ACB={38}^{\circ },then\angle AOBis$

• A.
  ${45}^{\circ }$
• B.
  ${19}^{\circ }$
• C.
  
  ${57}^{\circ }$
• D.
  ${76}^{\circ }$

Answer 1

The correct option is D

${76}^{\circ }$
We know that the angle subtended by an arc of a circle at the centre is double of the angle subtended by it at any point on the remaining part of the circle.



$\therefore \angle AOB=2\angle ACB\Rightarrow \angle AOB=2\times {38}^{\circ }={76}^{\circ }(\because \angle ACB={38}^{\circ })$

Hence, the correct answer is option (d).