To derive the formula for the sum of the interior angles of a regular polygon using the angle sum of triangles, we can use the following reasoning:
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Understanding the Angles of a Triangle: The sum of the interior angles of a triangle is always \(180^\circ\).
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Decomposing a Polygon: A polygon can be divided into triangles. For a regular polygon with \(n\) sides, you can draw diagonals from one vertex to all non-adjacent vertices. This creates \(n-2\) triangles.
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Calculating the Sum of Interior Angles: Since each triangle has an angle sum of \(180^\circ\), the total sum of the interior angles of a regular polygon with \(n\) sides can be calculated as follows: \[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
Now, let's apply this formula to find the sum of the interior angles of a square (\(n = 4\)):
\[ \text{Sum of interior angles} = (4 - 2) \times 180^\circ = 2 \times 180^\circ = 360^\circ \]
Thus, the sum of the angles of a square is:
The sum of the angles of a square is 360°.
In terms of your possible responses, the correct one is: "The sum of the angles of a square is 360 degrees."
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