Question

Show that the angles of an equilateral triangle is 60 degree each

Answer 1

sum of measure of all angle of triangle is 180
take any three angles
m<a +m<b+ m<c =180°
take all angles as x
x+x+x = 180
3x =180°
x=60
so, all the angles of triangle are 60°

Answer 2

For an equilateral triangle, we know that all 3 sides of the triangle are equal. Accordingly, all the 3 sides of the equilateral triangle hold equal angles.

Since, we know, that the sum of all angles of any triangle be 180° .

Let each angle be a.

Thus, $a+a+a=180^{\circ}$

$\begin{array}{l}{\Rightarrow \quad 3 a=180^{\circ}} \\ {\Rightarrow a=\frac{180^{\circ}}{3}} \\ {\Rightarrow a=60^{\circ}}\end{array}$

Hence, we can show that all the 3 angles of an equilateral triangle hold equal angles; i.e. 60°.