Question
In the given figure, express $a$ in terms of $b$
✓
Answer
In $\triangle A B C$,
$B C=B A$
$\therefore \angle B C A=\angle B A C$
and Ext. $\angle C B E=\angle B C A+\angle B A C$
$\Rightarrow a=\angle B C A+\angle B C A$
$\Rightarrow a=2 \angle B C A$ .........(i)
But $\angle A C B=180^{\circ}-b$ $\ldots \ldots . .(\because \angle A C D$ and $\angle A C B$ are linear pair $)$
$\Rightarrow \angle B C A=180^{\circ}-b$ ..........(ii)
$\begin{aligned} & \therefore a=2 \angle B C A=2\left(180^{\circ}-b\right) \\ & =360^{\circ}-2 b\end{aligned}$
$B C=B A$
$\therefore \angle B C A=\angle B A C$
and Ext. $\angle C B E=\angle B C A+\angle B A C$
$\Rightarrow a=\angle B C A+\angle B C A$
$\Rightarrow a=2 \angle B C A$ .........(i)
But $\angle A C B=180^{\circ}-b$ $\ldots \ldots . .(\because \angle A C D$ and $\angle A C B$ are linear pair $)$
$\Rightarrow \angle B C A=180^{\circ}-b$ ..........(ii)
$\begin{aligned} & \therefore a=2 \angle B C A=2\left(180^{\circ}-b\right) \\ & =360^{\circ}-2 b\end{aligned}$
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