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choose all answers that describe the polygon w x y z if
w x=x y=y z=z w, m \angle w=84^{\circ}, m \angle x=96^{\circ},
m \angle y=84^{\circ}, and m \angle z=96^{\circ}.
answer attempt 1 out of 2
\square parallelogram
\square quadrilateral
\square rectangle
\square rhombus
\square square
\square trapezoid
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Explanation:

Step1: Recall the definition of quadrilateral

A quadrilateral is a polygon with four sides. Since \(WXYZ\) has four sides (\(WX\), \(XY\), \(YZ\), \(ZW\)), it is a quadrilateral.

Step2: Recall the definition of rhombus

A rhombus is a quadrilateral with all sides equal. Given \(WX = XY=YZ = ZW\), it satisfies the side - length property of a rhombus. Also, a rhombus does not require all angles to be equal. Here, \(\angle W=84^{\circ}\), \(\angle X = 96^{\circ}\), \(\angle Y=84^{\circ}\), \(\angle Z = 96^{\circ}\), which is consistent with the angle properties of a non - square rhombus.

Step3: Check for parallelogram

In a parallelogram, opposite angles are equal. Here, \(\angle W=\angle Y = 84^{\circ}\) and \(\angle X=\angle Z=96^{\circ}\), but a parallelogram also has the property that consecutive angles are supplementary (\(\angle W+\angle X=84 + 96=180^{\circ}\), \(\angle X+\angle Y=96 + 84=180^{\circ}\), \(\angle Y+\angle Z=84+96 = 180^{\circ}\), \(\angle Z+\angle W=96 + 84=180^{\circ}\)). However, a rhombus is a special case of a parallelogram. But we are looking for all possible answers.

Step4: Check for rectangle

In a rectangle, all angles are \(90^{\circ}\). Since \(\angle W = 84^{\circ}\), \(\angle Y=84^{\circ}\), \(\angle Z = 96^{\circ}\), it is not a rectangle.

Step5: Check for square

In a square, all sides are equal and all angles are \(90^{\circ}\). Since angles are not \(90^{\circ}\), it is not a square.

Step6: Check for trapezoid

In a trapezoid, at least one pair of sides is parallel. A rhombus has two pairs of parallel sides (by the property of a parallelogram: if a quadrilateral is a rhombus, it is a parallelogram). But the key property that makes it not just a trapezoid is the all - side - equal property. A trapezoid does not require all sides to be equal. So the more specific and correct non - trapezoid answers are quadrilateral and rhombus.

Answer:

• B. Quadrilateral
• D. Rhombus