Question

In the given figure, chords $AB=CD,\angle COD={60}^{\circ }$ and $\angle AOD={170}^{\circ }$.

Find the value of $\angle BOC$.

• A. ${60}^{\circ }$
• B. ${70}^{\circ }$
• C. ${75}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is B

${70}^{\circ }$

We know that equal chords subtend equal angle at the centre.

$\Rightarrow \angle AOB=\angle COD={60}^{\circ }$

Since, the central angle of a circle is ${360}^{\circ }$

So, $\angle AOB+\angle BOC+\angle COD+\angle AOD={360}^{\circ }$

$\Rightarrow 60°+\angle BOC+60°+170°=360°$

$\Rightarrow 290°+\angle BOC=360°$

$\Rightarrow \angle BOC=360-290={70}^{\circ }$