Question

choose all answers that describe the polygon wxyz if wx = xy = yz = zw, m∠w = 84°, m∠x = 96°, m∠y = 84°, and m∠z = 96°. 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. Since $WXYZ$ has 4 sides, it is a quadrilateral.

Step2: Check for parallelogram properties

In a parallelogram, opposite - angles are equal. Here, $\angle W = 84^{\circ}$ and $\angle Y=84^{\circ}$, $\angle X = 96^{\circ}$ and $\angle Z = 96^{\circ}$, so it is a parallelogram.

Step3: Check for rhombus properties

A rhombus is a parallelogram with all sides equal. Given $WX = XY=YZ = ZW$, it is a rhombus.

Step4: Check for rectangle and square properties

A rectangle has all angles equal to $90^{\circ}$. Since the angles are $84^{\circ}$ and $96^{\circ}$, it is not a rectangle or a square.

Step5: Check for trapezoid properties

A trapezoid has one pair of parallel sides. Since it is a parallelogram (both pairs of opposite sides are parallel), it is not a trapezoid.

Answer:

A. Parallelogram
B. Quadrilateral
D. Rhombus