Of course, a quadrilateral can be constructed.
If you know the three angles, then you can easily find the fourth angle and the others sides will automatically get constructed if you join the four points while the two sides are already known.
A quadrilateral can be constructed uniquely if the lengths of its three sides and two diagonals are given.
A quadrilateral can be constructed uniquely if its two adjacent sides and three angles are given.
A quadrilateral can be constructed uniquely if its three sides and two included angles are given.