Question How many sides does a polygon have if the sum of the interior angles is \( 3240^{\circ} \) ? Answer Attempt 1 out of 2

To find the number of sides \( n \) of a polygon when given the sum of the interior angles, you can use the formula \( S = (n - 2) \times 180^\circ \). If \( S = 3240^\circ \), then: \[ 3240 = (n - 2) \times 180 \] By rearranging and solving for \( n \), we find \( n \). First, divide both sides by 180, giving \( 18 = n - 2 \). Adding 2 yields \( n = 20 \), meaning this polygon has 20 sides. Additionally, did you know that polygons have fascinating properties? For instance, a 20-sided polygon is called an "icosagon." Icosagons can be regular or irregular, and the regular icosagon has some intriguing symmetries, making it a popular shape in various designs, including art and architecture! If you've ever tackled geometry problems, you might have had a few missteps! A common pitfall is neglecting to correctly apply the formula for the sum of the interior angles, leading to incorrect calculations. Double-check your steps, ensuring you're using \( (n-2) \) correctly to prevent any confusion when identifying the number of sides. Happy calculating!