The sum of the interior angles of a regular polygon is .
How many sides does the regular polygon have?
sides

To find the number of sides of a regular polygon given that the sum of its interior angles is , you can use the formula:

where is the number of sides. Setting this equal to :

Dividing both sides by :

Adding 2 to both sides gives:

So, the polygon has sides.

A fun fact about nonagon (the nine-sided polygon) is that it has a beautifully unique aesthetic appeal. Often seen in various cultural art forms, the nonagon provides a canvas for creative designs, embodying symmetry and balance—qualities cherished throughout history!

In real-world applications, nonagons show up in architecture and design. Think about intricate tile patterns or floor designs that utilize this shape to create visually striking effects. Plus, in nature, the honeycomb structure of bee hives often displays hexagonal and pentagonal shapes, but you might also see nonagons if you’re lucky enough to come across a flower or plant with nine petals!