Question

choose all answers that describe the polygon qrst if m∠q = 88°, m∠r = 92°, m∠s = 88°, m∠t = 92°, \\(\overline{qr} \parallel \overline{st}\\), and \\(\overline{rs} \parallel \overline{tq}\\).

answer attempt 1 out of 2

• parallelogram
• quadrilateral
• rectangle
• rhombus
• square
• trapezoid

Explanation:

Step1: Identify polygon type by sides

QRST has 4 vertices, so it's a quadrilateral.

Step2: Check parallel sides

$\overline{QR} \parallel \overline{ST}$ and $\overline{RS} \parallel \overline{TQ}$: both pairs of opposite sides are parallel → parallelogram.

Step3: Check rectangle condition

Rectangle needs all right angles ($90^\circ$). Given angles are $88^\circ, 92^\circ$ → not right angles, so not rectangle.

Step4: Check rhombus/square conditions

Rhombus needs all sides equal (no info given); square needs right angles + equal sides → neither applies.

Step5: Check trapezoid condition

Trapezoid has only one pair of parallel sides → no, since two pairs are parallel.

Answer:

Quadrilateral, Parallelogram