Question

$O$ is the center of the circle. If $\angle OAB={20}^{\circ }$ and $\angle OCB={55}^{\circ }$, then the magnitude of $\angle BOC$ is:

• A. ${70}^{\circ }$
• B. ${60}^{\circ }$
• C. ${50}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is A ${70}^{\circ }$

In $△OCB$,

$OC=OB$ ...[Radius of a circle]

$\Rightarrow$ $\angle OCB=\angle CBO={55}^o$ ...[Angles opposite of equal sides are equal].

Then, $\angle OCB+\angle CBO+\angle BOC={180}^o$ ...[Angle sum property]

$\Rightarrow$ ${55}^o+{55}^o+\angle BOC={180}^o$

$\Rightarrow$ ${110}^o+\angle BOC={180}^o$

$\Rightarrow$ $\angle BOC={180}^o-{110}^o$

$\Rightarrow$ $\angle BOC={70}^o$.

Therefore, option $A$ is correct.