Constructing a parallelogram with a given angle and area equal to a given quadrilateral

In this exercise you are given a quadrilateral \(PQRS\), an angle \(\angle XYZ\) and a points \(S\). Your task is to construct a parallelogram with area equal to the area of \(PQRS\) and one pair of opposite angles equal to \(\angle XYZ\).

Once you are done you can use the polygon tool to highlight the parallelogram and then use the area tool to check that the area is equal to that of the quadrilateral \(PQRS\). You can also use the angle tool to check that one pair of interior angles of the parallelogram is equal to \(\angle XYZ\). The previous two constructions Constructing a parallelogram with area equal to a given triangle and Constructing a parallelogram with a given sidelength will be useful.

The diagram contains an example of a quadrilateral \(ABCD\) and an angle \(\angle EFG\) such that the orange parallelogram \(HIJK\) has area equal to that of \(ABCD\) and \(\angle KHI = \angle EFG\).

Hint. This exercise is explained in Euclid Book I, Proposition 45.