If we take the largest side (10) to be the base and we call the heigth h, then the area is given by 10h. But we know the area, so we can find h.
By drawing the parallellogram and this height, you can form a right triangle (at the left or right side of the parallellogram).
This right triangle has one side h (which we know now) and hypotenuse 6. With the pythagorean theorem, you can even find the last side.
Now you have this triangle and you know all sides, use some trigonometry to fnd the angles. For example, check this topic.