Question

In the adjoining figure, if the angles $\angle AOB,\angle BOC,\angle COD$ are in the ratio $1:2:3$ and $\overleftrightarrow{AD}$ is a straight line, find the measures of all the angles.

Answer 1

We know that
$\angle AOB+\angle BOC+\angle COD={180}^o$ .......... $\left(i\right)$

Let $\angle AOB=x$
But the given hypothesis is $\angle BOC=2\angle AOB=2x$ and $\angle COD=3\angle AOB=3x$.

From $\left(i\right)$, we get

$\angle AOB+2\angle AOB+3\angle AOB={180}^o$
Thus, we get $6x={180}^o$.
It follows that $\angle AOB=x={30}^o$.
This gives $\angle BOC=2\times {30}^o={60}^o$ and $\angle COD=3\times {30}^o={90}^o$.