<p>Given: A shape with 4 sides and no right angles, opposite sides are parallel, and some sides have different lengths.</p> <p>To identify the shape:</p> <p>1. The shape cannot be a rectangle or a square because they have right angles.</p> <p>2. It cannot be a hexagon because a hexagon has 6 sides.</p> <p>3. It cannot be a rhombus because all sides of a rhombus are of equal length.</p> <p>4. The only quadrilateral with parallel opposite sides and different lengths is a parallelogram.</p> <p>\textbf{The best name for Charlie's shape is "parallelogram".}</p>
The image displays a polygon, specifically a regular octagon since all sides appear to be of equal length and angles appear to be equal. In a regular octagon, each pair of sides that are opposite each other are parallel. Since an octagon has eight sides, it will have four pairs of opposite sides. Therefore, the number of pairs of opposite sides that are parallel in this regular octagon is four.
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