Given,

x>y hence angle opposite x will be greater than angle opposite y.

This is always true for any triangleLet the angle opposite y be

a. then

since this is a isoscles triangle the three angles would be x,x,a

There is another triangle rule that angles in triangle add to 180 degrees.A possible scenario for the three triangles above would be 70,70,40.

Let us see if we can have z less than 60 degrees.

If z was lets say 59 degree then 2z would be 118 degrees that leaves the third angle opposite to y (a) = 62 degrees

However angle a cannot be more than z.Notice that z cannot be 60 degree as that would make this triangle an equilateral triangle however a should be less than z.

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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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