Angles in a triangle

Consider an equilateral triangle ABC.

Given that $AB = BC = CA = 10\text{cm}.$

If $AB = BC$ ,

$\large \displaystyle \angle A = \angle B.$ (Angles opposite to equal sides are equal)

Similarly in case of all the angles.

$\large \displaystyle \therefore \angle A = \angle B = \angle C.$

We know that sum of all the angles in a triangle is $180^{\circ}.$

$\large \displaystyle \implies \angle A + \angle B + \angle C = 180^{\circ}.\\ \large \displaystyle \implies 3 \times \angle A = 180^{\circ}.$

$\large \displaystyle \implies \angle A = \frac{180}{3} = \color{#D61F06}{\boxed{60^{\circ}}}.$

$\large \displaystyle \therefore \angle A = \angle B = \angle C = \color{#3D99F6}{60^{\circ}}.$

Therefore, Each angle in an equilateral triangle measures $\large \displaystyle \color{#20A900}{60^{\circ}}.$

triangle is equilateral

Since the side lengths are equal, the angles are also equal. It is an equilateral triangle and in an equilateral triangle the measure of each interior angle is 60 degrees.