9. Why is the sum of the interior angles of a polygon always a multiple of 180 ?

Every polygon can be divided into triangles, and the sum of the interior angles of a triangle is always 180 degrees. For example, a quadrilateral can be divided into two triangles, creating two sets of 180 degrees, totaling 360 degrees, and so forth for polygons with more sides. Thus, you can generalize this to any polygon by using the formula (n-2) × 180, where n is the number of sides, proving the sum is always a multiple of 180. This concept has real-world applications in fields like architecture and engineering. When designing structures, understanding the properties of polygons, including the sum of their angles, helps professionals create stable and aesthetically pleasing structures. Whether it’s the roof of a building or the layout of a park, the knowledge of angle sums plays a critical role in ensuring the designs are not only functional but also visually appealing!