The Sum Of Interior Angles Of A Hexagon
Understanding the sum of interior angles of a hexagon is an important concept in geometry. A hexagon is a six-sided polygon, and the interior angles of a polygon are the angles on the inside of it. The sum of the interior angles of a hexagon is always equal to 720 degrees. In this article, we will explore the concept of interior angles of a hexagon in detail.
What are Interior Angles?
Interior angles are the angles on the inside of a polygon. In a hexagon, there are six interior angles. To find the interior angles of a hexagon, we can draw lines from one corner of the hexagon to all the other corners. This will create six triangles inside the hexagon. The interior angles of the hexagon are the angles inside these triangles.
How to Find the Measure of Each Interior Angle
To find the measure of each interior angle of a hexagon, we can use the formula:
Measure of each interior angle = (Sum of interior angles of hexagon) / 6
Since we know that the sum of interior angles of a hexagon is 720 degrees, we can substitute this value into the formula:
Measure of each interior angle = 720 / 6 = 120 degrees
Why is the Sum of Interior Angles of a Hexagon Always 720 Degrees?
The sum of interior angles of any polygon is always equal to the number of sides minus two, multiplied by 180 degrees. So for a hexagon, which has six sides, the formula would be:
Sum of interior angles of hexagon = (6 - 2) x 180 degrees = 4 x 180 degrees = 720 degrees
This formula can be used to find the sum of interior angles of any polygon, not just hexagons.
Properties of Interior Angles of a Hexagon
There are several properties of interior angles of a hexagon worth noting:
- The sum of any two adjacent interior angles of a hexagon is always 180 degrees.
- The sum of the exterior angles of a hexagon is always 360 degrees.
- The measure of each exterior angle of a hexagon is equal to 360 degrees divided by the number of sides, which in this case is 6. So each exterior angle of a hexagon measures 60 degrees.
Example Problems
Let's work through some example problems to help solidify our understanding of interior angles of a hexagon.
Example 1:
What is the measure of each interior angle of a regular hexagon?
Solution:
Since a regular hexagon has six equal sides and six equal angles, we can use the formula:
Measure of each interior angle = (Sum of interior angles of hexagon) / 6
Substituting in 720 for the sum of interior angles:
Measure of each interior angle = 720 / 6 = 120 degrees
So each interior angle of a regular hexagon measures 120 degrees.
Example 2:
What is the measure of one exterior angle of a regular hexagon?
Solution:
As mentioned earlier, each exterior angle of a hexagon measures 60 degrees, since there are six exterior angles in a hexagon:
360 degrees / 6 = 60 degrees
So each exterior angle of a regular hexagon measures 60 degrees.
Conclusion
In conclusion, the sum of interior angles of a hexagon is always equal to 720 degrees. We can use this fact, along with other properties of interior angles of a hexagon, to solve problems and better understand the geometry of shapes. Remember that the formula for finding the sum of interior angles of any polygon is (number of sides - 2) x 180 degrees, and that the measure of each interior angle of a hexagon is equal to the sum of interior angles divided by 6.
Keep exploring and learning!
Posting Komentar untuk "The Sum Of Interior Angles Of A Hexagon"