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 7th graders response , determine if quadrilateral QRST is a parallelogram, and if so, solve for x.

Question

What’s the answer (4 points)

Answer 1

To determine if quadrilateral QRST is a parallelogram, we need to check if the opposite angles are equal. Angle Q measures 108°, and Angle R measures 108 - 2x. Since the sum of the angles in a quadrilateral is 360°, we can set up the equation: 108 + (108 - 2x) + Angle S + Angle T = 360.

Now, we know that opposite angles in a parallelogram must be equal, so let's assume Angle S is also 108°, making Angle T = 360 - (108 + 108) = 144°. Now, solving for x: 108 - 2x = 144 gives us -2x = 36, so x = -18; however, this doesn’t give us a valid answer for x in a standard parallelogram. Thus, QRST is not a parallelogram.