Quadrilateral QRST has vertices at Q(−1,5) , R(2,8) , S(4,4) , and T(1,1) . The measure of Angle Q is 108° and the measure of angle R is 108−2x . In 3-5 sentences, determine if quadrilateral QRST is a parallelogram, and if so, solve for x.
To determine whether quadrilateral QRST is a parallelogram, we can compare the slopes of opposite sides. The slope of QR is (8-5)/(2-(-1)) = 1, and the slope of ST is (1-4)/(1-4) = 1. Since the slopes are equal, QR is parallel to ST. Similarly, we can calculate the slope of RS to be (4-8)/(4-2) = -2. Since the slopes of QR and RS are not equal, quadrilateral QRST is not a parallelogram.
Therefore, we cannot solve for x in this case.