To determine if quadrilateral QRST is a parallelogram, we need to check if the sum of the consecutive interior angles equals 360°. The angles at Q and R are given as 108° and \(108 - 2x\) respectively. Since opposite angles must be supplementary in a parallelogram, we set up the equation \(108 + (108 - 2x) + \text{Angle S} + \text{Angle T} = 360\). For QRST to be a parallelogram, the other two angles must also satisfy the supplementary angle condition.
To find x, we use the property that angles Q and R must add with angles S and T to equal 360°. Since we don't have angle S and angle T values, we can look at the provided angles. First, let's calculate the two consecutive angles. If we assume the sum of angles Q, R, S, and T equals 360 degrees, we can suggest that angle S is equal to angle Q and angle T equals angle R for simplicity of the analysis, i.e., \(x\) must equal a certain value offering equality.
By substituting \(x\) for angle R, we calculate that angle R must be supplementary to its own angle Q and should decrease \(2x\) in the framework of 360, leading us to values insufficient with no given remedy.
Thus, if angles S and T reflect equality or reflected measures of angles Q and R respectively, they must adjust to satisfy 360 without contradictions highlighting the need for more detail around angle scenarios. The implications can show that QRST is not a parallelogram as immediate contradiction in reliant values appears. Thus we don't yield a defined x for the resolution.
We conclude that QRST cannot be confirmed as a parallelogram without further disclosed angles S and T definitions or modeling angles revealing proper relationships around the cyclical measure needed.