In a rhombus, one diagonal is equal to a side. find the corners of the rhombus.

Since ABCD is a rhombus, the lengths of all its sides are equal, AB = AD = BC = CD.

By condition, the length of the diagonal BD is equal to the length of the side of the rhombus, then in the triangle ABD, AB = AD = BD, and therefore the triangle ABD is equilateral, and then all its internal angles are 60.

Angle BAD = ABD = ADB = 60.

The sum of the adjacent corners of the rhombus is 180, and the opposite angles are equal.

Then the angle BCD = BAD = 60, the angle ABC = ADC = 180 – 60 = 120.

Answer: 120, 60, 120, 60.