We know the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon
Dear student
The sum of interior angles of a polygon is given by
For a polygon of n sides, sum of angles = (n-2)
So, for a polygon of (n+1) sides, sum of angles =(n+1-2)=(n-1)
Difference = (n-1)-(n-2)= = constant
Hence the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression
For a polygon of 21 sides, sum of angles = (n-2)=sum of angles = (21-2)=19
Regards
The sum of interior angles of a polygon is given by
For a polygon of n sides, sum of angles = (n-2)
So, for a polygon of (n+1) sides, sum of angles =(n+1-2)=(n-1)
Difference = (n-1)-(n-2)= = constant
Hence the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression
For a polygon of 21 sides, sum of angles = (n-2)=sum of angles = (21-2)=19
Regards