Question

Prove that the angles in an equilateral triangle are $60^\circ $.

Answer 1

Hint: Equilateral triangles have three sides equal. This gives the three angles of the triangle are also equal. Sum of angles of any triangle is equal to $180^\circ $. Combining these we get the proof.

Formula used:
The sum of the angles in any triangle is equal to $180^\circ $.

Complete step-by-step answer:
To prove each of the three angles in an equilateral triangle is equal to $60^\circ $.
Equilateral triangle is the type of triangle with all the three sides equal.
We have three sides equal implies the three angles of the triangle are also equal.
Also we know that the sum of the angles in any triangle is equal to $180^\circ $.
This gives three times the angle of an equilateral triangle is equal to $180^\circ $.
Let each angle be $x$.
Now we can say $3x = 180^\circ $
So we have the angles of the equilateral triangle is equal to $\dfrac{{180^\circ }}{3} = 60^\circ $.

Additional information:
Equilateral triangle has other peculiarities as well.
In an equilateral triangle, in-centre and circum-centre coincide and circum-radius is twice the in-radius.
The perpendicular bisector of a side is also the angle bisector of the angle opposite to it.
The area of an equilateral triangle with side $a$ is given by $\dfrac{{\sqrt 3 {a^2}}}{4}$.

Note: We can draw equilateral triangles with any measurement for sides. Anyway the angles remain constant and equal to $60^\circ $. In the other way we can say that if the three angles of a triangle are $60^\circ $, then the triangle is equilateral.