Question
Find all the angles of an equilateral troiangle.
✓
Answer
In $\triangle\text{ABC},$ we have $\text{AB}=\text{AC}$
$\Rightarrow \angle\text{C}=\angle\text{B}\ ...(\text{i})$
$\text{BC}=\text{AC}$
$\angle\text{A}=\angle\text{B}\ ...(\text{ii})$
Now, $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}$
$\Rightarrow \angle\text{A}+\angle\text{A}+\angle\text{A}=180^{\circ}$
$\Rightarrow 3\angle\text{A}=180^{\circ}$
$\Rightarrow \angle\text{A}=\frac{180^{\circ}}{3}=60^{\circ}$
$\therefore \angle\text{A}=\angle\text{B}=\angle\text{C}=60^{\circ}$
$\Rightarrow \angle\text{C}=\angle\text{B}\ ...(\text{i})$
$\text{BC}=\text{AC}$
$\angle\text{A}=\angle\text{B}\ ...(\text{ii})$
Now, $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}$
$\Rightarrow \angle\text{A}+\angle\text{A}+\angle\text{A}=180^{\circ}$
$\Rightarrow 3\angle\text{A}=180^{\circ}$
$\Rightarrow \angle\text{A}=\frac{180^{\circ}}{3}=60^{\circ}$
$\therefore \angle\text{A}=\angle\text{B}=\angle\text{C}=60^{\circ}$
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