Question

choose all answers that describe the polygon pqrs if m∠p = 78°, m∠q = 78°, m∠r = 102°, m∠s = 102°, and $overline{pq}paralleloverline{rs}$. answer attempt 1 out of 2 parallelogram quadrilateral rectangle rhombus square trapezoid

Explanation:

Step1: Recall polygon definitions

A quadrilateral is a four - sided polygon, and $PQRS$ has 4 sides.

Step2: Analyze parallel sides

Since $\overline{PQ}\parallel\overline{RS}$, and it has 4 sides, it is a trapezoid (a trapezoid has at least one pair of parallel sides).

Step3: Check for parallelogram properties

In a parallelogram, opposite angles are equal. Here, $\angle P=\angle Q = 78^{\circ}$ and $\angle R=\angle S=102^{\circ}$, and $\overline{PQ}\parallel\overline{RS}$. The sum of adjacent angles $\angle P+\angle R=78^{\circ}+ 102^{\circ}=180^{\circ}$ and $\angle Q+\angle S=78^{\circ}+102^{\circ}=180^{\circ}$, so it is also a parallelogram.

Step4: Check for rectangle, rhombus and square

A rectangle has all angles equal to $90^{\circ}$, so it is not a rectangle. A rhombus has all sides equal (no information about side - lengths is given to suggest this), and a square is both a rectangle and a rhombus, so it is neither a rhombus nor a square.

Answer:

A. Parallelogram
B. Quadrilateral
F. Trapezoid