Question

In the given figure, $OA=AB=BC=CD=OD$. Find the measure of $\angle AOD$.

• A. $46^{\circ }$
• B. $36^{\circ }$
• C. $63^{\circ }$
• D. $49^{\circ }$

Answer 1

Answer: (B)

$OA=AB=BC=CD=OD$
Let $\angle O=x$
As $AO=AB,\angle O=\angle ABO=x$
$\Rightarrow \angle CAB=\angle O+\angle ABO=2x$
As $AB=BC,\angle CAB=\angle BCA=2x$
As $OD=DC,\angle O=\angle OCD=x$
$\angle CDB=\angle O+\angle OCD=2x$
$\text{ As }CD=CB,\angle CDB=\angle CBO=2x$
$\text{ In }DOCB,\angle O+\angle BCO+\angle CBO=180^{\circ }$
$\Rightarrow x+2x+2x=180^{\circ }$
$\Rightarrow 5x=180^{\circ }\Rightarrow x=36^{\circ }$