Question

'$O$' is the centre of a circle, $\angle BOA={90}^o$ and $\angle COA={110}^o$. Find the measure of $\angle BAC$.

• A. ${70}^o$
• B. ${80}^o$
• C. ${120}^o$
• D. ${50}^o$

Answer 1

Answer: (B)

${80}^o$

From the diagram.
$\angle BOA=90°$
$\angle COA=110°$
We know that in the center of the circle angle is $360°$
$\angle COB=360°-90°+110°$
$=360°-200°$
$=160°$
$\angle COB=2\angle CAB$
$160°=2\angle CAB$
$\angle CAB=\frac{160°}{2}=80°$

$\therefore \angle BAC={80}^{\circ }$