Question

In the given figure O is the centre of circle. If $\angle OAB={30}^{\circ }$ and $\angle OCB={40}^{\circ }$, then measure of $\angle AOC$ is :

• A. ${70}^{\circ }$
• B. ${220}^{\circ }$
• C. ${140}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

Answer: (C)

${140}^{\circ }$

Consider $△OAB$ and $△OBC$

$OA=OB\Rightarrow \angle OAB=\angle OBA={30}^o$

$OB=OC\Rightarrow \angle OCB=\angle OBC={40}^o$

So, $\angle ABC=\angle OBA+\angle OBC={70}^o$

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

$\angle AOC=2\angle ABC={140}^o$

So option C is the right answer.