Understanding The Sum Of Angles In Heptagon
The heptagon is a seven-sided polygon that has always been an interesting subject among math enthusiasts. In this article, we will discuss the sum of angles in heptagon, its properties, and how to calculate it. So, if you are curious about this topic, then keep on reading.
Properties of Heptagon
Before we delve into the sum of angles in heptagon, let us first discuss some of its properties.
A heptagon has seven sides and seven angles. All its angles are equal in measure, which means that each angle of a regular heptagon measures 128.571 degrees.
A heptagon can also be classified as a convex polygon. This means that all its interior angles are less than 180 degrees.
Calculation of Sum of Angles in Heptagon
Now, let us move on to the main topic of this article, which is the sum of angles in heptagon.
To calculate the sum of angles in heptagon, we first need to know the formula for finding the sum of interior angles of any polygon. The formula is:
Sum of Interior Angles = (n - 2) x 180 degrees
where n is the number of sides of the polygon.
Using this formula, we can calculate the sum of angles in heptagon as follows:
Sum of Interior Angles = (7 - 2) x 180 degrees
Sum of Interior Angles = 5 x 180 degrees
Sum of Interior Angles = 900 degrees
Therefore, the sum of angles in heptagon is 900 degrees.
Proof of Sum of Angles in Heptagon
Now that we know the formula for calculating the sum of angles in heptagon, let us prove it.
We can divide a heptagon into five triangles, as shown below:
Each of these triangles has an angle sum of 180 degrees. Therefore, the sum of angles in the heptagon is equal to the sum of angles in these five triangles.
Sum of Angles in Heptagon = Sum of Angles in 5 Triangles
Sum of Angles in Heptagon = 5 x 180 degrees
Sum of Angles in Heptagon = 900 degrees
Hence, the formula we used earlier to calculate the sum of angles in heptagon is proven.
Conclusion
In conclusion, we have discussed the sum of angles in heptagon, its properties, and how to calculate it. We have also proven the formula for finding the sum of angles in heptagon using a simple geometric method.
Understanding the sum of angles in heptagon is important not only for math enthusiasts but also for those who are interested in geometry and other related fields. We hope that this article has helped you gain a better understanding of this topic.
So, go ahead and explore the fascinating world of heptagons!
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