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in ∆ BAD
AB = AD
Angle ADB = Angle ABD
(because angle opposite to equal sides are equal)
let the angle as "x"
since ADB = ABD so
ADB + ABD = 2x
and Angle BAD = 60°
so sum of angle of a triangle
60° + x +x = 180°
2x = 180° - 60°
2x = 120°
x = 60°
this means that all angles are equal so all sides are also equal.
so
AD=DB=AB=60 cm
similarly
DC=CB=DB=60 cm
(since diagonals of a parallelogram are equal)
so diagonals are
60 cm and 60 cm
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