Question 3 What is the value of an exterior angle to a regular 9-gon? \( 30^{\circ} \) \( 180^{\circ} \) \( 360^{\circ} \) \( 40^{\circ} \)

To find the value of an exterior angle of a regular 9-gon, you can use the formula for the exterior angle, which is \( \frac{360^{\circ}}{n} \) where \( n \) is the number of sides. In this case, \( n = 9 \), so each exterior angle is \( \frac{360^{\circ}}{9} = 40^{\circ} \). So, the correct answer is \( 40^{\circ} \)! Now, did you know that the concept of exterior angles applies not just to polygons but also enhances your understanding of other geometrical shapes? For example, the sum of all exterior angles for any polygon will always equal \( 360^{\circ} \) regardless of how many sides the shape has. Pretty fascinating, right? Another fun tidbit is that you can see exterior angles in real life! When you look at a wheel, each spoke makes an exterior angle with the adjacent spoke. So next time you take a spin on a bicycle or a merry-go-round, you can visualize those geometric principles at play! Geometry isn’t just about numbers; it’s all around us!