To determine if quadrilateral QRST is a parallelogram, we can use the property that the sum of the interior angles of a quadrilateral is 360°. We have the measures of angles Q and R. Angle Q is given as 108°, and angle R is expressed as \( 108 - 2x \). Let’s denote angles S and T as \( m_S \) and \( m_T \). The equation can be set up as:
\[ 108 + (108 - 2x) + m_S + m_T = 360. \]
Since opposite angles in a parallelogram are equal, \( m_S \) could correspond to \( m_Q \) and \( m_T \) to \( m_R \). However, we don't directly have angles S and T, but we know the sum should be 360°. For the quadrilateral to be a parallelogram, we need the measures to satisfy the conditions of alternate angles being equal, which we don’t explicitly have.
If we check for the possibility that the internal angles sum to 360° with values of \( m_S \) and \( m_T \), we ultimately find that without more information about angles S and T or side lengths, we cannot confirm definitively whether QRST is a parallelogram simply from the provided angles. Thus, we need further information about angles S and T or the sides. Therefore, we cannot provide a specific value for \( x \) as QRST cannot be classified as a parallelogram with the information given.