Question

show that angle of an equilateral triangle are 60° each

Answer 1

Hey mate!
Here is your answer
Let us consider,
ABC be an equilateral triangle



BC = AC = AB (Length of all sides is same)

∠A = ∠B = ∠C (Sides opposite to the equal angles are equal)

Also,

∠A + ∠B + ∠C = 180° ( Sum of interior angles of a triangle is 180°)

3∠A = 180°

∠A = 60°

Therefore,

∠A = ∠B = ∠C = 60°

Thus,

The angles of an equilateral triangle are 60° each
Hope it helps

Answer 2

Hello mate ^_^

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Solution:

∆ABC is equilateral which means that

AB=BC=AC.

AB=AC means that ∠B=∠C                  (In triangle, angles opposite to equal sides are equal)  .....(1)

AB=BC means that ∠A=∠C         (In triangle, angles opposite to equal sides are equal) ...... (2)

From (1) and (2), we can say that

∠A=∠B=∠C                                     .........(3)

Also, ∠A+∠B+∠C=180°             (Angle sum property of triangle)

Putting (3) in the above equation, we get

∠A+∠A+∠A=180°

⇒3∠A=180°

⇒∠A=180/3=60°                .......(4)

From (3) and (4), we can say that

∠A=∠B=∠C=60°

hope, this will help you.

Thank you______❤

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