Question
In the given figure, find $\angle A O B$ and $\angle B O C$.
✓
Answer
In the figure,
$5 x+x+80^{\circ}+123^{\circ}+85^{\circ}=360^{\circ} \ldots . .($ Angles at a point $)$
$ \Rightarrow 6 \mathrm{x}+80^{\circ}+123^{\circ}+85^{\circ}=360^{\circ} $
$ \Rightarrow 6 x+288^{\circ}=360^{\circ} $
$ \Rightarrow 6 \mathrm{x}=360^{\circ}-288^{\circ}=72^{\circ} $
$ \Rightarrow \mathrm{x}=\frac{72^{\circ}}{6}=12^{\circ} $
Now, $\angle A O B=5 x=5 \times 12^{\circ}=60^{\circ}$
and $\angle B O C=x=12^{\circ}$
$5 x+x+80^{\circ}+123^{\circ}+85^{\circ}=360^{\circ} \ldots . .($ Angles at a point $)$
$ \Rightarrow 6 \mathrm{x}+80^{\circ}+123^{\circ}+85^{\circ}=360^{\circ} $
$ \Rightarrow 6 x+288^{\circ}=360^{\circ} $
$ \Rightarrow 6 \mathrm{x}=360^{\circ}-288^{\circ}=72^{\circ} $
$ \Rightarrow \mathrm{x}=\frac{72^{\circ}}{6}=12^{\circ} $
Now, $\angle A O B=5 x=5 \times 12^{\circ}=60^{\circ}$
and $\angle B O C=x=12^{\circ}$
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