How Many Degrees Does A Decagon Have?
Welcome to our blog post where we will discuss a mathematical concept that has always been intriguing to many. In this article, we will be talking about how many degrees does a decagon have. For those who are not familiar, a decagon is a polygon with ten sides and ten angles.
The Formula for Calculating the Total Degrees of a Decagon
To calculate the total degrees of a decagon, we need to use a formula that is applicable to all polygons. The formula is:
Total degrees = (n-2) x 180
In this formula, "n" represents the number of sides of the polygon. Therefore, to find the total degrees of a decagon, we substitute "n" with 10:
Total degrees = (10-2) x 180
Total degrees = 8 x 180
Total degrees = 1440
Thus, the total degrees of a decagon is 1440.
The Measure of Each Angle in a Decagon
Now that we know the total degrees of a decagon, we can calculate the measure of each angle. To do this, we use the formula:
Measure of each angle = Total degrees / Number of angles
As we know that a decagon has ten angles, we can substitute the values in the formula:
Measure of each angle = 1440 / 10
Measure of each angle = 144
Therefore, each angle in a decagon measures 144 degrees.
The Internal and External Angles of a Decagon
The internal angles of a decagon are the angles formed inside the shape, while the external angles are formed outside the shape. To calculate the measure of each internal angle, we use the formula:
Measure of each internal angle = (n-2) x 180 / n
Substituting the values:
Measure of each internal angle = (10-2) x 180 / 10
Measure of each internal angle = 144
Thus, each internal angle in a decagon measures 144 degrees. Similarly, to calculate the measure of each external angle, we use the formula:
Measure of each external angle = 360 / n
Substituting the values:
Measure of each external angle = 360 / 10
Measure of each external angle = 36
Thus, each external angle in a decagon measures 36 degrees.
Properties of a Decagon
A decagon has several properties that are worth mentioning. Some of these are:
- A decagon has ten sides and ten angles.
- The sum of all interior angles of a decagon is 1440 degrees.
- The measure of each interior angle of a decagon is 144 degrees.
- The measure of each exterior angle of a decagon is 36 degrees.
- A decagon has 35 diagonals.
Real-Life Applications of a Decagon
Decagons are not commonly found in everyday life. However, they can be seen in various fields such as:
- Architecture: Decagons are used in the design of buildings, especially in the construction of domes.
- Geometry: Decagons are used in geometry to understand the properties of polygons and their angles.
Conclusion
In conclusion, a decagon is a polygon with ten sides and ten angles. The total degrees of a decagon is 1440, and each angle measures 144 degrees. The internal and external angles of a decagon measure 144 degrees and 36 degrees, respectively. Decagons have several properties and can be seen in various fields such as architecture and geometry.
Thank you for reading our article. We hope that you found it informative and useful.
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