Let the acute angle be A and obtuse angle be B.
Rhombus ABCD, and angle A = angle C = acute angles.
The perpendicular from B to AD be BE.
Now in ÎABE, AE = ED = AB/2 = AD/2
cos A = AE/AB = 1/2
angle A = 600 = angle C
angle B = angle D = (360 - 2x60)/2 = 1200.