Question

choose all answers that describe the polygon below.
answer attempt 1 out of 2
parallelogram
quadrilateral
rectangle
rhombus
square

Explanation:

• Quadrilateral: A quadrilateral is a four - sided polygon. The given figure has four sides, so it is a quadrilateral.
• Parallelogram: In a parallelogram, consecutive angles are supplementary (their sum is \(180^{\circ}\)). \(77^{\circ}+103^{\circ}=180^{\circ}\) and \(83^{\circ}+97^{\circ}=180^{\circ}\). Also, if one pair of opposite sides is parallel (indicated by the arrows on \(r\) and \(q\)), and consecutive angles are supplementary, it satisfies the properties of a parallelogram.
• Not a rectangle: A rectangle has all angles equal to \(90^{\circ}\). The angles in the given polygon are \(77^{\circ},83^{\circ},97^{\circ},103^{\circ}\), so it is not a rectangle.
• Not a rhombus: A rhombus has all sides equal. There is no information given about the side lengths being equal.
• Not a square: A square is a special case of a rectangle and a rhombus (all angles \(90^{\circ}\) and all sides equal). Since it is not a rectangle or a rhombus, it is not a square.

Answer:

Parallelogram, Quadrilateral