Question

Show that each angle of a equilateral triangle are 60° each .​

Answer 1

Answer:

This is can be easily proved by using the properties known about equilateral triangle

we know that all angle of equilateral triangle are equal

and sum of all angles of triangle is 180

let measure of one angle of equilateral triangle be x

so rest two angle becomes x and x

by using property

x+x+x=180

3x=180

x=60

so angle of equilateral triangle is 60

hope it helps

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Answer 2

Given:

• ABC is an equilateral triangle.

AB=BC=AC

TO Prove:

• Angle A = Angle B = Angle C = 60°

Proof:

• AB = AC
• ➪Angle C = Angle B

Also,

• AC = BC
• ➪Angle B = Angle A

From (1) & (2)

Angle A = Angle B = Angle C

In triangle ABC,

Angle A + Angle B + Angle C = 180°

Angle A + Angle A + Angle A = 180°

➪Angle 3a = 180°

➪Angle A = 180/30 = 60°

Therefore,

• Angle A = Angle B = Angle C = 60°

Hence Proved✔