Question

Is it true that all the angles of an equilateral triangle are equal? If so, what is each angle's measurement?

• A. No
• B. Yes, ${50}^{\circ }$
• C. Yes, ${60}^{\circ }$
• D. None of the above

Answer 1

The correct option is C Yes, ${60}^{\circ }$


In $△ABC,$
$AB=BC=CA$------(1)
[All sides of an equilateral triangle are equal]
From equation (1), $AB=BC$
$\therefore △ABC$ can be taken as an isosceles triangle
$⟹\angle C=\angle A$-------(2)
[Angles opposite to equal side of an isosceles triangle are equal]
Similarly from equation (1), $BC=CA$
$⟹\angle A=\angle B$-------(3)
Now, from (2) & (3), $\angle A=\angle B=\angle C$

Hence, all the angles of equilateral triangles are equal.

As we know, Sum of all the angles of a triangle = ${180}^{\circ }$
$⟹\angle A+\angle B+\angle C={180}^{\circ }$
$⟹3\angle A={180}^{\circ }$
$⟹\frac{3\angle A}{3}=\frac{{180}^{\circ }}{3}$
$⟹\angle A={60}^{\circ }$

$⟹\angle A=\angle B=\angle C={60}^{\circ }$