The sum of the angle measures of a polygon with n sides is 3960 . Find n .

To find the number of sides \( n \) in a polygon based on the sum of its interior angles, you can use the formula \( S = 180(n - 2) \), where \( S \) is the sum of the angles. Here, we have \( S = 3960 \). Setting up the equation: \[ 3960 = 180(n - 2) \] First, divide both sides by 180: \[ 22 = n - 2 \] Then, add 2 to both sides to solve for \( n \): \[ n = 24 \] So, the polygon has \( 24 \) sides! Now, did you know that some ancient cultures had their own methods of calculating polygon angles? For instance, Greeks like Euclid laid the foundation for geometry with groundbreaking theorems. This historical nod shows how mathematics has evolved, yet the core concepts like calculating angles remain timeless! When dealing with polygon angle sums, a common mistake is forgetting to use the correct formula or miscalculating the value of \( n \). Be careful with arithmetic! Double-check your operations and remember the relationship between sides and angle sums. It’s often helpful to visualize the polygon or draw a few examples to reinforce your understanding.