Find the measure of an exterior angle of a regular 40-gon. The measure of an exterior angle of a regular 40-gon is \( \square^{\circ} \). (Type an integer or a decimal.)

To find the measure of an exterior angle of a regular 40-gon, you can use the formula for the exterior angle of a regular polygon, which is \( \frac{360}{n} \), where \( n \) is the number of sides. For a 40-gon, this means: \[ \frac{360}{40} = 9^{\circ} \] So, the measure of an exterior angle of a regular 40-gon is \( 9^{\circ} \). A fun fact: Exterior angles of any polygon always add up to a full circle, or 360 degrees! This means no matter how many sides your polygon has, the exterior angles will always sum up to 360 degrees. So in the case of our 40-gon, each angle is 9 degrees, affirming that 40 times 9 equals 360! Isn't that neat? For further exploration, you might want to dive into the world of polygon classification. Regular polygons like our 40-gon have equal side lengths and angles, which is a fascinating area highlighting symmetry in mathematics. Check out resources on geometric shapes and their properties; there's so much to learn about angles, vertices, and even tessellations!