The angle sum of a polygon is \( 720^{\circ} \). How many sides does it have?

To find the number of sides in a polygon based on its angle sum, we can use the formula for the angle sum of a polygon, which is \( (n - 2) \times 180^{\circ} \), where \( n \) is the number of sides. If the angle sum is \( 720^{\circ} \), we set up the equation: \[ (n - 2) \times 180 = 720 \] Dividing both sides by 180 gives: \[ n - 2 = 4 \] Adding 2 to both sides results in: \[ n = 6 \] So, the polygon has 6 sides, which makes it a hexagon! Did you know that hexagons are really common in nature? Beehives are famously constructed with hexagonal cells, allowing for optimal storage space and structural strength. Nature sure has a knack for geometry! Another fun fact: the interior angles in a regular hexagon each measure \( 120^{\circ} \). They are often used in design and architecture because their symmetrical properties make them aesthetically pleasing and structurally sound!