Subjects geometry

Sum Interior Angles

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1. **Problem Statement:** Find the sum of the interior angles of a regular polygon with 7 sides (a heptagon). 2. **Formula:** The sum of the interior angles $S$ of a polygon with $n$ sides is given by: $$S = (n - 2) \times 180$$ This formula works because any polygon can be divided into $(n-2)$ triangles, and each triangle has an angle sum of 180 degrees. 3. **Apply the formula:** For a heptagon, $n = 7$. $$S = (7 - 2) \times 180 = 5 \times 180$$ 4. **Calculate:** $$S = 900$$ 5. **Interpretation:** The sum of the interior angles of a heptagon is 900 degrees. **Final answer:** The sum of the interior angles of the polygon is $900$ degrees.