Each exterior angle of a regular polygon measures \( 45^{\circ} \). How many sides does the polygon have? A. 8 B. 15 C. 10 D. 12

To determine the number of sides in the polygon, we can use the fact that the sum of all exterior angles of any polygon is \(360^{\circ}\). Since each exterior angle measures \(45^{\circ}\), we divide \(360^{\circ}\) by \(45^{\circ}\): \[ \text{Number of sides} = \frac{360^{\circ}}{45^{\circ}} = 8. \] So, the polygon has 8 sides. Now, let's look at the application of regular polygons in real life. Regular octagons, for instance, can be seen in stop signs! The design is not only distinctive but ensures that the sign is easily recognizable from a distance, enhancing safety. Knowing the properties of polygons helps in understanding architectural designs, geometry-related problem-solving, and even when creating art! For those interested in diving deeper, consider exploring works on geometry and regular polygons. Books like "Geometry: Euclid and Beyond" by Robin Hartshorne discuss the fundamentals of shapes and their properties, while engaging with both historical and theoretical perspectives. These resources can expand your understanding of not just polygons, but the very principles that govern our spatial world!