Find the number of diagonals of

(i) a hexagon,


(ii) a decagon,


(iii) a polygon of 18 sides


For a diagonal to be formed, 2 vertices are required. Thus in a polygon, there are 10 sides. And no. of lines can be formed are nC2, but in nC2 the sides are also included. N of them is sides.


Thus the no. of diagonals are nC2 - n


(i) hexagon


n=6


so no of diagonal is 6C2-6
= 9


(ii) decagon


n= 10


so no of diagonal is 10C2-10


= 35


(iii) N= 18


so no of diagonal is 18C2-18


= 135


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