Question

In the given figure, O is the centre of the circle, and $\angle OAB={20}^{\circ }$ and $\angle OCB={50}^{\circ }$. Find $\angle AOC$.

• A. ${20}^{\circ }$
• B. ${60}^{\circ }$
• C. ${70}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

OA = OC (radii of the same circle)
$\angle OAB=\angle OBA={20}^{\circ }$
In $\Delta OAB$,
$\angle OAB+\angle AOB+\angle BOA={180}^{\circ }$
${20}^{\circ }+{20}^{\circ }+\angle BOA={180}^{\circ }$
$\angle BOA={140}^{\circ }$
$OB=OC$ (radii of the same circle)
$\angle OBC=\angle OCB={50}^{\circ }$
In $\Delta OCB$,
$\angle OBC+\angle OCB+\angle COB={180}^{\circ }$
${50}^{\circ }+{50}^{\circ }+\angle COB={180}^{\circ }$
$\angle COB={80}^{\circ }$
$\angle AOB=\angle AOC+\angle BOC$
$\angle AOC=\angle AOB-\angle BOC$
$\angle AOC={140}^{\circ }-{80}^{\circ }$
$\angle AOC={60}^{\circ }$