Question

Show that each angle of an equilateral triangle is 60°.
Let A ABC be an equilateral triangle.​

Answer 1

Answer:

Given:

$The \ triangle \ is \ equilateral$

Solution:

$\triangle ABC \ is \ equilateral$

$\therefore \angle A = \angle B = \angle C$

$\angle A + \angle B + \angle C = 180^o$

$\implies \angle A + \angle A + \angle A = 180^o$

$\implies 3\angle A = 180^o$

$\implies \angle A = 60^o$

$\therefore \angle A = \angle B = \angle C = 60^o$

Answer 2

Figure:-

Given:-

• ABC be an equilateral triangle.

To find:-

• Show that each angle of an equilateral triangle is 60°.

Solutions:-

• Let the consider that ABC is an equilateral triangle.

Therefore,

AB = BC = AC

<C = <B ⠀⠀⠀⠀⠀⠀(Angle opposite to the equal side of the a triangle are equal)

Also,

AC = BC

<B = <A⠀⠀⠀⠀⠀⠀(Angle opposite to the equal side of the a triangle are equal)

Therefore,

<A = <B = <C

In ∆ABC,

<A + <B + <C = 180°

<A + <A + <A = 180°

3<A = 180°

<A = 180°/3

<A = 60°

<A = <B = <C = 60°

Hence, An equilateral triangle, all interior angle are measure 60°.

Some Important:-

• Scalene Triangle:- A triangle has all three sides of different lengths is a scalene triangle. All the three sides are of different lengths, the three angles are also be different.

• Isosceles Triangle:- A triangle has two sides of the same length and the third side of a different length is an isosceles triangle. The angles opposite the equal sides measure the same.

• Equilateral Triangle:- A triangle has all the three sides of the same length is an equilateral triangle. All the three sides are of the same length, all the three angles are also be equal. Each interior angle of an equilateral triangle = 60°.