Let ABCD be a rhombus such that the length of its diagonal BD is equal to the length of one of its sides.
That is, AB = BC = CD = AD = BD
∴△ABD is an equilateral triangle.
So, ∠BAD=60∘
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⇒∠BCD=60∘ [Opposite angles of a parallelogram are equal]
∠BAD+∠ABC=180∘ [Adjacent angles of a parallelogram are supplementary]
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⇒∠ABC=180∘−60∘=120∘
∠ADC=∠ABC=120∘ [Opposite angles of a parallelogram are equal]
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