Question

choose all answers that describe the polygon rstu if m∠r = 85°, m∠s = 95°, m∠t = 85°, m∠u = 95°, (overline{rs}paralleloverline{tu}), and (overline{st}paralleloverline{ur}). answer attempt 1 out of 2 parallelogram quadrilateral rectangle rhombus square trapezoid

Explanation:

Step1: Recall polygon definitions

A polygon with 4 sides is a quadrilateral. Here, $RSTU$ has 4 - sides, so it is a quadrilateral.

Step2: Check parallel - side condition

Since $\overline{RS}\parallel\overline{TU}$ and $\overline{ST}\parallel\overline{UR}$, by the definition of a parallelogram (a quadrilateral with both pairs of opposite sides parallel), $RSTU$ is a parallelogram.

Step3: Analyze angle measures

A rectangle has all angles equal to $90^{\circ}$. Since $m\angle R = 85^{\circ}$, $m\angle S=95^{\circ}$, $m\angle T = 85^{\circ}$, $m\angle U = 95^{\circ}$, it is not a rectangle. A square is a special - case of a rectangle with all sides equal, so it is not a square either. A rhombus has all sides equal, and there is no information about side - lengths being equal, so it is not a rhombus. A trapezoid has only one pair of parallel sides, but here both pairs of opposite sides are parallel, so it is not a trapezoid.

Answer:

A. Parallelogram
B. Quadrilateral