Question

Question 1
Find all the angles of an equilateral triangle.

Answer 1

Let ABC be an equilateral triangle such that AB=BC=CA
We have,$AB=AC\Rightarrow \angle C=\angle B$ [angle opposite to equal sides are equal]
Let $\angle C=\angle B=x^{\circ }.....\left(i\right)$
Now, BC=BA
$\Rightarrow \angle A=\angle C......\left(ii\right)$ [anlges opposite to equal sides are qual]
From eq.(i) and (ii)
$\angle A=\angle B=\angle C=x$
Now, in $\Delta ABC,\angle A+\angle B+\angle C={180}^{\circ }$ [by angle sum property of a triangle]
$\Rightarrow x+x+x={180}^{\circ }\Rightarrow 3x={180}^{\circ }\Rightarrow x={60}^{\circ }$
Hence, $\angle A=\angle B=\angle C={60}^{\circ }$