Question

In the given figure, $\angle$COD is a right angle, $\angle$AOC and $\angle$BOD are in the ratio of $3:2$. Then $\angle$BOD measures ___________.

• A. ${40}^o$
• B. ${50}^o$
• C. ${54}^o$
• D. ${36}^o$

Answer 1

The correct option is D ${36}^o$

As we can see from the figure, $\angle AOC+\angle COD+\angle DOB={180}^{\circ }\dots eqn\left(1\right)$

It is given, $\angle COD={90}^{\circ }$

and $\frac{\angle AOC}{\angle BOD}=\frac{3}{2}$

$\angle AOC=\frac{3}{2}\angle BOD$

Putting values in eqn (1), we get

$\Rightarrow 1.5\angle BOD+90+\angle BOD=180\Rightarrow 2.5\angle BOD=90\Rightarrow \angle BOD={36}^{\circ }$