We know that the sum of the interior angles of a triangle is`180^0`. S – InterviewSolution

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1.	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 ofa 21 sided polygon.
Answer» 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)` `=18019` `=3420`.

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