Question
Find each angle shown in the diagram.
✓
Answer
In the figure,
$3 \frac{1}{2} y ^{\circ}+2 y ^{\circ}+2 y ^{\circ}+2 \frac{1}{2} y ^{\circ}=360^{\circ}
....($Angles at a point$)$
$\Rightarrow \frac{7}{2} y^{\circ}+2 y^{\circ}+2 y^{\circ}+\frac{5}{2} y^{\circ}=360^{\circ}$
$\Rightarrow \frac{7}{2} y^{\circ}+\frac{5}{2} y^{\circ}+4 y^{\circ}=360^{\circ}$
$\Rightarrow \frac{12}{2} y^{\circ}+4 y^{\circ}=360^{\circ}$
$\Rightarrow 6 y^{\circ}+4 y^{\circ}=360^{\circ}$
$\Rightarrow 10 y^{\circ}=360^{\circ}$
$\Rightarrow y=\frac{360^{\circ}}{10}=36^{\circ}$
$ \therefore \angle \mathrm{AOB}=3 \frac{1}{2} \mathrm{y}^{\circ}=\frac{7}{2} \mathrm{y}^{\circ}=\frac{7}{2} \times 36^{\circ}$
$ =126^{\circ}$
$ \angle \mathrm{BOC}=2 \mathrm{y}^{\circ}=2 \times 36^{\circ}=72^{\circ}$
$ \angle \mathrm{COD}=2 \mathrm{y}^{\circ}=72^{\circ}$
$ \angle \mathrm{DOA}=2 \frac{1}{2} \mathrm{y}^{\circ}=\frac{5}{2} \mathrm{y}^{\circ}$
$ =\frac{5}{2} \times 36^{\circ}=90^{\circ} $
$3 \frac{1}{2} y ^{\circ}+2 y ^{\circ}+2 y ^{\circ}+2 \frac{1}{2} y ^{\circ}=360^{\circ}
....($Angles at a point$)$
$\Rightarrow \frac{7}{2} y^{\circ}+2 y^{\circ}+2 y^{\circ}+\frac{5}{2} y^{\circ}=360^{\circ}$
$\Rightarrow \frac{7}{2} y^{\circ}+\frac{5}{2} y^{\circ}+4 y^{\circ}=360^{\circ}$
$\Rightarrow \frac{12}{2} y^{\circ}+4 y^{\circ}=360^{\circ}$
$\Rightarrow 6 y^{\circ}+4 y^{\circ}=360^{\circ}$
$\Rightarrow 10 y^{\circ}=360^{\circ}$
$\Rightarrow y=\frac{360^{\circ}}{10}=36^{\circ}$
$ \therefore \angle \mathrm{AOB}=3 \frac{1}{2} \mathrm{y}^{\circ}=\frac{7}{2} \mathrm{y}^{\circ}=\frac{7}{2} \times 36^{\circ}$
$ =126^{\circ}$
$ \angle \mathrm{BOC}=2 \mathrm{y}^{\circ}=2 \times 36^{\circ}=72^{\circ}$
$ \angle \mathrm{COD}=2 \mathrm{y}^{\circ}=72^{\circ}$
$ \angle \mathrm{DOA}=2 \frac{1}{2} \mathrm{y}^{\circ}=\frac{5}{2} \mathrm{y}^{\circ}$
$ =\frac{5}{2} \times 36^{\circ}=90^{\circ} $
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