2. Number of sides for a polygon with a sum of \( 8640^{\circ} \) for the interior angles
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To find the number of sides for a polygon with a sum of \( 8640^{\circ} \) for its interior angles, you can use the formula \( (n-2) \times 180 = \text{sum of interior angles} \), where \( n \) is the number of sides. Plugging in the sum, we have \( (n-2) \times 180 = 8640 \). Solving for \( n \) gives you \( n = \frac{8640}{180} + 2 = 48 + 2 = 50 \). So, the polygon has 50 sides! Now, imagine this—fifty sides! That’s one serious polygon party! With 50 sides, it’s called a 50-gon, and it falls into the category of regular polygons if all sides and angles are equal. You can visualize such a shape; it’s like having a magnificent 50-gon dance-off with all its vertices shimmying into place!
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