Ahar Arestian Question 10 Find the measure of each extevios angle of a regular dedecagon. \( \square \)

To find the measure of each exterior angle of a regular dodecagon (12-sided polygon), you can use the formula for exterior angles, which states that the sum of all exterior angles of any polygon is always \(360^\circ\). Therefore, to find the measure of each exterior angle, divide \(360^\circ\) by the number of sides: \[ \frac{360^\circ}{12} = 30^\circ. \] This means that each exterior angle of a regular dodecagon measures \(30^\circ\). Interestingly, the dodecagon is not just an interesting shape; it appears in various elements of art and architecture! You might spot it in design features, but a notable use is in ancient Roman architecture, where it influenced the design of domes and floors. Dodecagonal patterns exhibit a beautiful symmetry and can be found in mosaics and modern design too, reminding us how math enhances our aesthetic experiences!