Q. 43.8( 6 Votes )

In regular polygo

Answer :

Let us consider a regular polygon.


We know how to calculate the sum of all its interior angles.


s = 180 (n – 2)


Where, s = sum


N is the number of sides of the regular polygon


Let us use this formula for a triangle:


For a triangle, n = 3


So, s = 180 × (3 – 2)


= 180 × 1


= 180


Let us use this formula for a square:


For a square, n = 4


So, s = 180 × (4 – 2)


= 180 × 2


= 360


Let us use this formula for a pentagon:


For a square, n = 5


So, s = 180 × (5 – 2)


= 180 × 3


= 540


Let us tabulate the results:



From the above table we can see that s/n is not a constant. So, s is not proportional to n.


Let us modify the formula


Let s = 180 × m


Where s = sum


M = (n-2)


N is the number of side of the regular polygon



We can see that s is proportional to m. The constant of proportionality is 180


In ordinary language, we can say this:


The sum of interior angle of a regular polygon is proportional to ‘2 less than the number of sides’.


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