Question

Show that the angles of an equilateral triangle are ${60}^{\circ }$ each.

Answer 1

In equilateral triangle all sides are equal, so $AB=BC=AC$.

Since, we have angles opposite to equal sides are equal.

So, $AC=AB$

$\Rightarrow \angle C=\angle B$ .......(i)
Similar way, for $CA=CB$ $\Rightarrow \angle B=\angle A$........(ii)
From equation(i) and (ii), we can write $\angle A=\angle B=\angle C$
In a triangle, sum of three angles would be equal to ${360}^{\circ }$

$\angle A+\angle B+\angle C={180}^{\circ }$

$\Rightarrow \angle A+\angle A+\angle A={180}^{\circ }$

$3\angle A={180}^{\circ }$

$\therefore \angle A={60}^{\circ }$.
Hence, each angle of an equilateral triangle is ${60}^{\circ }$