Fact 1: a quadrilateral with two pairs of equal opposite angles is a parallelogram. (Because then the opposite sides are parallel.)

>AND SIDES

Fact 2: a quadrilateral with two pairs of equal opposite sides is a parallelogram. (Because of SSS when you draw one of the diagonals.)

There is a quadrilateral with two pairs of equal sides: a kite. It does have a pair of opposite equal angles.

BUT IT'S NOT PARALLELOGRAMME;

Not every kite is a parallelogram.

Maybe you are talking of something three-dimensional?

First I consider our potential quadrilateral like a four bar mechanism with two bars of equal length, I called them R1 and R2 .

The two other bars, without loosing generalization one I can draw horizontal I named it L, and the other remaining bar joining the two other edges of bars R1 and R2 , I called it B.

I called p the angle between R1 and L , and I called q the angle between R2 and L, both angles measured with a counterclockwise criteria , and I made q > p.

I called w the angle formed by B and L, it is obvious w equal to q - p

Now we take the horizontal and vertical projections of the polygonal represented by the four bars mechanism it will render the two following equations:

B cos (w) = R2 cos(q) - R1 cos (p) + L (1)
B sin (w) = R2 sin (q) - R1 sin (p) (2)

Since R1 equal R2 we can consider both as unit length then L and B will represent the ratio L/R and B/R

By division of the above equations and sub sequential ordering we get

cot (w) = (cos(q) - cos (p) + L) / (sin (q) - sin (p))

Remembering w = q-p now we can write

L = cos (p) - cos (q) + (sin (p) - sin (q)) cot (q-p)

So with this handy formula let us say we want to draw a quadrilateral two opposing side equal to 100 mm and the opposing angles forming p = 30 degrees and for example q = 45 degrees that will give us a value for L = 93.185 mm. and value for B amounts 80.02 mm