Interior Angles of a Polygon
by Daisy, Aug 18 2023
What is a Polygon?
A polygon is a simple shape we see around us, like rectangles, squares, and triangles. It's flat and has only two dimensions – length and width.
Imagine polygon as a flat picture on a paper. When we connect dots on its edges, we make straight lines called sides. Where these sides meet, we have angles called interior angles.
The number of sides in a polygon tells us how many interior angles it has. For example, a triangle has three sides and three interior angles. A square has four sides and four interior angles.
The Sum of the Interior Angles of a Polygon
Finding the sum of interior angles of a polygon is like discovering a secret code in math. It's all connected to triangles! You see, a triangle has three sides, and its interior angles add up to 180 degrees. The cool thing is that this works for all triangles, no matter their sizes.
Now, here's the exciting part – for any polygon with "p" sides, we can find its sum of interior angles using a simple formula: (p - 2) times 180 degrees. This formula is like a magic rule that gives us the sum of interior angles for any polygon.
Examples of Shapes and their Sum of Interior Angles
Let's explore more examples of regular shapes and their corresponding sums of interior angles using the formula.
Regular Polygons:
Regular polygons have a special charm because all their sides are of equal length, making them incredibly symmetrical. They are like perfect shapes that are pleasing to the eye. Here are some additional examples of regular polygons and their sum of interior angles:
- Regular Hexagon (6 sides): The sum of interior angles is (6 - 2) × 180 degrees = 720 degrees.
- Regular Heptagon (7 sides): The sum of interior angles is (7 - 2) × 180 degrees = 900 degrees.
- Regular Octagon (8 sides): The sum of interior angles is (8 - 2) × 180 degrees = 1080 degrees.
- Regular Nonagon (9 sides): The sum of interior angles is (9 - 2) × 180 degrees = 1260 degrees.
- Regular Decagon (10 sides): The sum of interior angles is (10 - 2) × 180 degrees = 1440 degrees.
As you can see, for any regular polygon, the formula (p - 2) × 180 degrees gives us the sum of its interior angles. Regular polygons are like a family of shapes, and the formula helps us find their secret sum of angles.
Irregular Polygons:
Now, let's take a look at more irregular polygons, which have sides of different lengths, giving them unique appearances. Again, the formula works for these shapes, and the sum of interior angles remains constant, even if the angles themselves vary.
For instance, consider an irregular heptagon. It has seven sides, so the sum of interior angles is (7 - 2) × 180 degrees = 900 degrees. Even though the sides are not equal in length, the sum of its interior angles is still 900 degrees.
In conclusion, understanding polygons and their interior angles is like uncovering the magic of geometry. Using the formula, we can find the sum of interior angles for any polygon. Whether they are regular wonders like the equilateral triangle or irregular shapes with unique side lengths, the formula guides us to discover the secrets of each polygon's angles. So next time you see a polygon in a picture, drawing, or anything else, you'll know how to find its hidden angles and appreciate the fun of geometry!