Find all the anlges of an equilateral triangle.

Explanation

Let ABC be an equilateral triangle such that AB=BC=CA
We have, `AB=AC rArr angleC=angleB`
[angle opposite to equal sides are equal ]

` "Let" " "angleC=angleB=x^(@) " "….(i)`
` NOW, " "BC=BA `
`rArr " "angleA=angleC " "...(ii)`
[angle oposite to equal sides are equal ]
From Eqs. (i) and (ii) ,
`angleA=angleB=angleC=x`
Now in `Delta ABC," "angleA+angleB+angleC=180^(@) " "["by angle sum property of a triangle "]`
`rArr " "x+x+x=180^(@)`
`rArr " "3x=180^(@)`
`because" "x=60^(@)`
Hence `angleA=angleB=angleC=60^(@)`