Question

For the diagram above, if $\angle 1$ is twice the value of $\angle 2$, then $\angle 2=$

• A. ${30}^{\circ }$
• B. ${20}^{\circ }$
• C. ${40}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$


Given: $\angle 1=2\times \angle 2$ and $\angle AOD={90}^{\circ }$.

Since, $\angle AOD,\angle COD,\angle BOC$ are all lying on a straight line,
$\Rightarrow \angle AOD+\angle DOC+\angle COB={180}^{\circ }$

$\Rightarrow {90}^{\circ }+\angle 2+\angle 1={180}^{\circ }$
$\Rightarrow {90}^{\circ }+\angle 2+2\angle 2={180}^{\circ }$
$\Rightarrow 3\angle 2={180}^{\circ }-{90}^{\circ }={90}^{\circ }$
$\Rightarrow 3\angle 2={90}^{\circ }\Rightarrow \angle 2={30}^{\circ }$
$\therefore \angle 2={30}^{\circ }$