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 sentences in 5th graders response , determine if quadrilateral QRST is a parallelogram, and if so, solve for x. And what is the answer. (4 points)

Answer 1

To see if quadrilateral QRST is a parallelogram, we need to check if the opposite angles add up to 180 degrees. Since Angle Q is 108°, we can find Angle S by using Angle Q and Angle R. If Angle R is 108 - 2x and Angle S is 72°, we can add that up with Angle Q to see if it makes 180°: 108° + (108 - 2x) = 180°. By solving this, we find that x = 12. So, quadrilateral QRST is a parallelogram with x equal to 12!