Question
In the adjoining figure, if $b^{\circ}=a^{\circ}+c^{\circ}$, find $b$.
✓
Answer
$a ^{\circ}+ b ^{\circ}+ c ^{\circ}=180^{\circ} \text {............(straight angle) } $
$\text { But } b ^{\circ}= a ^{\circ}+ c ^{\circ} \ldots . . . . \text { (given) } $
$\therefore a ^{\circ}+ c ^{\circ}+ b ^{\circ}=180^{\circ} $
$\Rightarrow b ^{\circ}+ b ^{\circ}=180^{\circ} $
$\Rightarrow 2 b ^{\circ}=180^{\circ} $
$\Rightarrow b ^{\circ}=\frac{180^{\circ}}{2}=90^{\circ}$
Hence $b^{\circ}=90^{\circ}$
$\text { But } b ^{\circ}= a ^{\circ}+ c ^{\circ} \ldots . . . . \text { (given) } $
$\therefore a ^{\circ}+ c ^{\circ}+ b ^{\circ}=180^{\circ} $
$\Rightarrow b ^{\circ}+ b ^{\circ}=180^{\circ} $
$\Rightarrow 2 b ^{\circ}=180^{\circ} $
$\Rightarrow b ^{\circ}=\frac{180^{\circ}}{2}=90^{\circ}$
Hence $b^{\circ}=90^{\circ}$
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