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 degrees 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

To determine if quadrilateral QRST is a parallelogram, we can use the property that in a parallelogram, the sum of opposite angles must be equal to 180 degrees. We are given that the measure of angle Q is 108 degrees and the measure of angle R is \(108 - 2x\).

According to the properties of a parallelogram, we have:

\[ \angle Q + \angle R = 180^\circ \]

Substituting the known angles:

\[ 108 + (108 - 2x) = 180 \]

Simplifying this equation:

\[ 216 - 2x = 180 \] \[ -2x = 180 - 216 \] \[ -2x = -36 \] \[ x = 18 \]

Since we found a consistent solution for \(x\), we conclude that quadrilateral QRST is indeed a parallelogram, and \(x = 18\).