What is the value of an exterior angle to a regular 9-gon? \( 30^{\circ} \) \( 180^{\circ} \) \( 360^{\circ} \) \( 40^{\circ} \)

The value of an exterior angle of a regular polygon can be found using the formula \( \frac{360^\circ}{n} \), where \( n \) is the number of sides. For a regular 9-gon, that would be \( \frac{360^\circ}{9} = 40^\circ \). So, the correct choice is \( 40^{\circ} \)! Did you know that the concept of exterior angles extends beyond polygons? In fact, the idea can be applied in architecture and design, where understanding the angles can lead to more aesthetically pleasing and structurally sound creations. So next time you admire a building, think about those angles! As you explore geometry, remember to keep an eye out for common misconceptions. A frequent mistake is confusing exterior angles with interior angles, which can lead to wrong calculations. Always visualize or draw the polygon; it helps solidify the differences and keep your angles in check!