Question

In the given figure, $O A=A B=B C=C D=O D$. Find the measure of $\angle A O D$.

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

Answer 1

Answer: (B)

$O A=A B=B C=C D=O D$
Let $\angle O =x$
As $A O=A B, \angle O =\angle A B O=x$
$\Rightarrow \angle C A B=\angle O +\angle A B O=2 x$
As $A B=B C, \angle C A B=\angle B C A=2 x$
As $O D=D C, \angle O =\angle O C D=x$
$\angle C D B=\angle O +\angle O C D=2 x $
$ \text { As } C D=C B, \angle C D B=\angle C B O=2 x $
$ \text { In } D O C B, \angle O+\angle B C O+\angle C B O=180^{\circ} $
$\Rightarrow x+2 x+2 x=180^{\circ} $
$ \Rightarrow 5 x=180^{\circ} \Rightarrow x=36^{\circ}$