If so, you’ve come to the right place. In this article, we will explore the concept of exterior angles and discuss how to calculate them efficiently. So, let’s dive in and unravel the secrets of polygons!

What is an exterior angle?

An exterior angle of a polygon is formed when one side of the polygon is extended. It is the angle between this extended side and the adjacent side of the polygon.

How can we calculate the measure of an exterior angle?

The measure of an exterior angle of any polygon can be calculated using a simple formula: 360 degrees divided by the number of sides in the polygon. Let’s take a few examples to understand this better.

How do we calculate the exterior angle of a triangle?

A triangle has three sides, so we divide 360 degrees by 3. Therefore, each exterior angle of a triangle measures 120 degrees.

What about squares and rectangles?

Both squares and rectangles have four sides, so we divide 360 degrees by 4. The exterior angle of a square or a rectangle measures 90 degrees.

Can we find the exterior angle of a pentagon?

Certainly! A pentagon has five sides, so each exterior angle measures 360 degrees divided by 5, which is 72 degrees.

How about hexagons and heptagons?

A hexagon has six sides, and each exterior angle is 360 degrees divided by 6, which equals 60 degrees. Similarly, a heptagon has seven sides, resulting in exterior angles of 360 degrees divided by 7, which is approximately 51.43 degrees.

What if we have a polygon with more sides, like an octagon or a decagon?The calculation remains the same. An octagon has eight sides, resulting in exterior angles measuring 360 degrees divided by 8, or 45 degrees. A decagon, with ten sides, gives us exterior angles of 360 degrees divided by 10, which equals 36 degrees.

Is there any pattern we can observe?

Yes, indeed! As we increase the number of sides in a polygon, the measure of each exterior angle decreases. The sum of all exterior angles in any polygon is always 360 degrees, regardless of the number of sides it has.

Do these calculations work for irregular polygons as well?

These calculations only apply to regular polygons, meaning all sides and angles are equal. For irregular polygons, we would have to measure each exterior angle individually.

Now that we have a clear understanding of how to find the exterior angle of a polygon, we can apply this knowledge to various shapes. Whether it’s a triangle, square, pentagon, or any other regular polygon, we can effortlessly determine the measure of its exterior angles using the simple formula.

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