Question

Show that the angles of an equilateral triangle are 60° each.

Answer 1

Let the angles be x, y and z

Now by angle sum property

x + y + z = 180

Since, all the angles in equilateral triangle are equal so

x = y = z

Put x in place of y and z.

x + x + x = 180

3x = 180

x = 180 / 3

x = 60

Since x = y = z

So, x = 60, y = 60, z = 60

Hence proved


Regards

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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