Its not stated that the shape is a parallelogram, so the shape could be something like a trapezoid. Knowing something about two of the interior angles doesn't tell us anything about the rest, and we therefore do not know anything about the lengths of the diagonals; 1 does not hold.
Based on 2, we know that the shape must be a rhombus, but we don't know anything about the interior angles; 2 does not hold.
Together, we know that the same is a rhombus and which of the angles are large/small -- we can therefore answer the question; C.
Nice explanation! Thanks:)