Polygon With N Sides Formula: Everything You Need To Know In 2023

Februari 21, 2023 Posting Komentar

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Welcome to our guide on the polygon with n sides formula. In this article, we'll take you through everything you need to know about calculating the interior and exterior angles of a polygon with n sides. Whether you're a student, mathematician, or just someone curious about the world of geometry, we've got you covered.

What is a Polygon?

Before we dive into the formula, let's first define what a polygon is. A polygon is a two-dimensional shape that is made up of straight lines and angles. The most common polygons are triangles, squares, and rectangles, but polygons can have any number of sides.

Calculating the Interior Angle of a Polygon

One of the most common questions when it comes to polygons is how to calculate the interior angle. The formula to do so is:

Interior Angle = (n-2) x 180 / n

Where n is the number of sides in the polygon.

Let's take a pentagon (a polygon with 5 sides) as an example. Using the formula, we can calculate the interior angle as:

Interior Angle = (5-2) x 180 / 5 = 108 degrees

So, the interior angle of a regular pentagon is 108 degrees.

Calculating the Exterior Angle of a Polygon

Another common question is how to calculate the exterior angle of a polygon. The exterior angle is the angle between a side of the polygon and an adjacent side extended outward. The formula to calculate the exterior angle is:

Exterior Angle = 360 / n

Using the same example of a pentagon, we can calculate the exterior angle as:

Exterior Angle = 360 / 5 = 72 degrees

So, the exterior angle of a regular pentagon is 72 degrees.

Calculating the Sum of Interior Angles of a Polygon

Another interesting property of polygons is that the sum of the interior angles is always (n-2) x 180 degrees. This means that the sum of the interior angles of a triangle is 180 degrees, the sum of the interior angles of a quadrilateral is 360 degrees, and so on.

To calculate the sum of the interior angles of a polygon, we can use the formula:

Sum of Interior Angles = (n-2) x 180

So, for a pentagon, we have:

Sum of Interior Angles = (5-2) x 180 = 540 degrees

Types of Polygons

Polygons can be classified into different types based on their number of sides and angles. Some common types of polygons include:

Triangle: 3 sides, 3 angles
Quadrilateral: 4 sides, 4 angles
Pentagon: 5 sides, 5 angles
Hexagon: 6 sides, 6 angles
Heptagon: 7 sides, 7 angles
Octagon: 8 sides, 8 angles
Nonagon: 9 sides, 9 angles
Decagon: 10 sides, 10 angles

Conclusion

There you have it, everything you need to know about the polygon with n sides formula. We hope this article has helped you understand the basics of polygons, and how to calculate their interior and exterior angles. Remember to always double-check your calculations, and don't be afraid to ask for help if you're stuck. Happy calculating!