Question

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.​

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if quadrilateral QRST is a parallelogram, we need to compare their corresponding sides and opposite angles. The measure of Angle Q is given as 108°, which is equal to the measure of Angle S since they are opposite angles. This suggests that QRST may be a parallelogram. Now, we know that the measure of Angle R is 108-2x. If QRST is a parallelogram, the measure of Angle R should also be equal to the measure of Angle T. Thus, we can set up the equation: 108-2x = 180° - 108° = 72°. Solving this equation gives us x = 18. Hence, for QRST to be a parallelogram, x should equal 18.