1. **State the problem:** We are given a polygon with sides 16, 32, 32, and 16 units, opposite sides equal and parallel, and pairs of opposite angles equal. We need to identify which polygon types describe this shape. 2. **Analyze the properties:** - Opposite sides are equal and parallel (16 opposite 16, 32 opposite 32). - Opposite angles are equal. - Adjacent sides have different lengths (16 and 32). 3. **Recall polygon definitions:** - **Parallelogram:** Quadrilateral with both pairs of opposite sides parallel. - **Quadrilateral:** Any four-sided polygon. - **Rectangle:** Parallelogram with four right angles. - **Rhombus:** Parallelogram with all sides equal. - **Square:** Parallelogram with all sides equal and four right angles. - **Trapezoid:** Quadrilateral with at least one pair of parallel sides. 4. **Apply definitions to the polygon:** - Since opposite sides are parallel and equal, it is a parallelogram. - It is a quadrilateral by definition. - Sides are not all equal (16 and 32), so it is not a rhombus or square. - No information about right angles, so cannot confirm rectangle or square. - It has two pairs of parallel sides, so it is not a trapezoid (which has only one pair). 5. **Final conclusion:** The polygon is a parallelogram and a quadrilateral only. **Answer:** Parallelogram, Quadrilateral