Welcome to our lesson on calculating angles in hexagons! A hexagon is a polygon with six sides. We'll learn about interior and exterior angles, and see the difference between regular and irregular hexagons. Let's start by examining this regular hexagon where all sides and angles are equal.
Now let's learn the formula for calculating the sum of interior angles in any polygon. The formula is: sum equals n minus 2, times 180 degrees, where n is the number of sides. For a hexagon with 6 sides, we calculate: 6 minus 2, times 180 degrees, which equals 4 times 180 degrees, giving us 720 degrees total.
In a regular hexagon, all sides are equal and all angles are equal. To find each interior angle, we divide the total sum by the number of sides. So each angle equals 720 degrees divided by 6, which gives us 120 degrees. Notice the equal marks on the sides showing they are all the same length, and each interior angle measures exactly 120 degrees.
Now let's explore exterior angles. An exterior angle is formed by extending one side of the polygon. The sum of all exterior angles in any polygon is always 360 degrees. For a regular hexagon, each exterior angle equals 360 degrees divided by 6, which is 60 degrees. Notice the important relationship: interior angle plus exterior angle always equals 180 degrees. We can verify this: 120 degrees plus 60 degrees equals 180 degrees.
To summarize what we've learned about hexagon angles: The sum of interior angles uses the formula n minus 2 times 180 degrees. For a hexagon, this gives us 720 degrees total. In a regular hexagon, each interior angle measures 120 degrees, and each exterior angle measures 60 degrees. Remember that interior and exterior angles always add up to 180 degrees.