Hexagon Sum Of Interior Angles

Introduction:

 Polygon is the word which is derived from the Greek language which is nothing but the 2- dimensional closed plane figure .It is formed using the line segments which are termed as sides or edges. Depending on the number of sides, the polygons are  classified as:triangle(3 sides), quadrilateral(4 sides), pentagon(5 sides), hexagon (6 sides) and so on. Thus, Hexagon can be defined as the closed polygon with six sides having interior and exterior angles.

The Interior angle of a polygon can be defined as the angle which constitute to form inside the 2 -dimensional shape.The sum of interior and exterior angles together add to 180 degrees.From the figure below, the interior angle which is inside equal to 30 degrees.

exterior angle - interior angle

 

Sum of Interior angles in Regular Polygon:

 

Sum of interior angles of a Regular Polygon:

The interior angle also depends on the type of polygon, whether it is regular or irregular. For a regular polygon all the interior angles are same , but for irregular polygon they are different.The general formula for finding sum of interior angles of a regular polygon is:

        sum = 180* (n-2) degrees, where 'n' is number of sides

Now , for a regular hexagon, which has six number of sides i,e n=6

sum of interior angles of regular hexagon   = 180 (n-2)  =180* (6-2)                                                                                                                                                                                    = 180 (4)                                                                                                                                                                                      =   720 degrees.

Hence, from this the sum of interior angles depends only on number of sides 'n' . 

 

Individual Interior angle of a Polygon:

 

 

regular hexagon

Each individual interior angle can be calculated using:

180*`(n-2)/(n)` degrees,where 'n' is number of sides of a polygon .

For regular Hexagon (n=6) each interior angle   =  180 * `(6-2)/(6)`   = 180 * `(4)/(6)`     = 30*4 = 120

 

Now ,we can recheck from this , that sum of interior angles of a regular hexagon  = 120+120+120+120+120+120=  720 degrees.              

These formulae would be applicable only in the case of Regular Hexagon , but not for irregular Hexagon.