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.​(4 points)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if quadrilateral QRST is a parallelogram, we need to compare the opposite sides and opposite angles. If the opposite sides are equal in length and the opposite angles are congruent, then the quadrilateral is a parallelogram. In this case, we can calculate the lengths of the sides QR, RS, ST, and TQ using the distance formula. If they are all equal, we can proceed to check the angles. If angle Q is 108° and angle R is 108-2x, we need to check if angle R is also equal to 108°. If it is, then the quadrilateral is a parallelogram. We can set up the equation 108-2x = 108 and solve for x to determine its value.

Answer 2

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