Question

We know that the sum of the interior angles of a triangle is`180^0` . 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 of a 21 sided polygon.

Answer 1

We, know that sum of the interior angles of n-sides=`180*(n-2)`
`a_n=180(n-2)`
`a_(n-1)=180((n-1)-2)`
`a_n-a_(n-1)=180(n-2)-180((n-1)-2)`
`a_n-a_(n-1)=180(n-2-n+1+2)`
`=180`
`d=180`
Sum of angles`=180(n-2)`
`=180*19`
`=3420`.