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The Angle-Sum Formula for a Polygon

publish date: 2026/05/16 08:22:27.188775 UTC

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The sum \(S\) of the measures of the angles of a polygon with \(n\) sides is given by the formula:

\[ S = (n - 2) \cdot 180° \]

What does the variable \(n\) represent in this formula?

s₁s₂s₃s₄s₅n = 5 sidesS = (5−2)·180° = 540°

Correct Answer

The number of sides of the polygon

Explanation

In the formula \(S = (n-2) \cdot 180°\), n is the number of sides of the polygon and S is the total sum of the interior angle measures in degrees. The expression \((n-2)\) gives the number of non-overlapping triangles the polygon can be divided into, each contributing 180°.

Reference

Mathematics for college students

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