Question
In $\triangle ABC; AB = AC$ and $\angle A :\angle B = 8 : 5;$ find $\angle A.$
✓
Answer
Let $\angle A=8 x$ and $\angle B=5 x$
Given: $A B=A C$
$\Rightarrow \angle B=\angle C=5 x \quad...($Angles opp. to equal sides are equal$)$
Now,
$\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^{\circ}$
$ \Rightarrow 8 \mathrm{x}+5 \mathrm{x}+5 \mathrm{x}=180^{\circ}$
$ \Rightarrow 18 \mathrm{x}=180^{\circ}$
$ \Rightarrow \mathrm{x}=10^{\circ}$
Given that:
$\angle \mathrm{A}=8 \mathrm{x}$
$ \Rightarrow \angle \mathrm{A}=8 \times 10^{\circ}$
$ \Rightarrow \angle \mathrm{A}=80^{\circ}$
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