Understanding The Sum Of Interior Angles Of A Hexagon
Are you struggling with understanding the concept of the sum of interior angles of a hexagon? Fear not, as we will be breaking down the topic for you in this article! By the end of this article, you will have a clear understanding of this fundamental concept in geometry.
What is a Hexagon?
A hexagon is a six-sided polygon that is made up of six straight lines or sides. It is a popular shape that can be found in nature, such as honeycombs and snowflakes, and in man-made structures like nuts and bolts.
What are Interior Angles?
Interior angles are angles that are inside a polygon. In a hexagon, the interior angles are the angles that are formed inside the six sides of the hexagon.
How to Calculate the Sum of Interior Angles of a Hexagon
To find the sum of the interior angles of a hexagon, we use a simple formula:
(n-2) x 180
Where n is the number of sides of the polygon. In this case, n=6 since we are dealing with a hexagon.
Substituting the value of n in the formula, we get:
(6-2) x 180 = 4 x 180 = 720
Therefore, the sum of the interior angles of a hexagon is 720 degrees.
Why is the Sum of Interior Angles of a Hexagon Important?
The sum of interior angles of a hexagon is an important concept in geometry. It helps us understand the relationship between the sides and angles of a polygon. It also enables us to calculate the measure of each interior angle of a hexagon.
Properties of the Sum of Interior Angles of a Hexagon
Here are some important properties of the sum of interior angles of a hexagon:
- The sum of the interior angles of a hexagon is always 720 degrees.
- Each interior angle of a regular hexagon measures 120 degrees.
- The sum of any two opposite interior angles of a hexagon is 180 degrees.
Examples of Using the Sum of Interior Angles of a Hexagon
Let's look at some examples of how we can use the sum of interior angles of a hexagon:
Example 1:
Find the measure of each interior angle of a regular hexagon.
Solution:
Since a regular hexagon has six equal sides and angles, we can divide the sum of the interior angles (720 degrees) by the number of angles in a hexagon (6).
Each interior angle of a regular hexagon measures:
720 ÷ 6 = 120 degrees
Example 2:
Find the measure of angle A in the hexagon below:
Solution:
Since the sum of the interior angles of a hexagon is 720 degrees, we can use this information to find the measure of angle A.
First, we add up the measures of the angles that are already given:
120 + 110 + 100 + 90 = 420
Then, we subtract this sum from the total sum of interior angles of a hexagon:
720 - 420 = 300
Therefore, the measure of angle A is 300 degrees.
Conclusion
The sum of interior angles of a hexagon is a fundamental concept in geometry. It helps us understand the relationship between the sides and angles of a polygon, and enables us to calculate the measure of each interior angle of a hexagon. By using the formula (n-2) x 180, we can easily find the sum of the interior angles of any polygon, including a hexagon.
So, the next time you come across a hexagon, you will have no trouble finding the sum of its interior angles!
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