The diagonal of the rhombus is d and d√3. Find the corners of the rhombus.

The diagonals of the rhombus are at right angles.
So the triangle AOB, like the others, is rectangular.
The diagonals of the rhombus are halved, which means:
OB = 1 / 2BD = a / 2
AO = 1 / 2AC = √3a / 2
By the Pythagorean theorem:
AB = √ (a / 2) squared + (√3a / 2) squared = √a squared / 4 + 3a squared / 4 = √4a squared / 4 = a
That is, the side of the rhombus is equal to the diagonal BD.
And triangle ABD is equilateral.
From this it follows that angle A = angle C = 60 degrees.
The angles adjacent to either side of the rhombus add up to 180 degrees.
So angle B = angle D = 180 degrees-angle A = 180-60 = 120 degrees
Answer: 60 degrees, 120 degrees.