Question

In the figure, O is the centre of the circle with $\angle AOB={85}^{\circ }and\angle AOC={115}^{\circ },then\angle BAC$ is :

• A. ${115}^{\circ }$
• B. ${85}^{\circ }$
• C. ${80}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is C ${80}^{\circ }$

$\angle BOC=360-115-85={160}^o$

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

$\angle BAC=\frac{1}{2}\angle BOC={80}^o$

So option C is the right answer.