(i) A heptagon has seven angular points and seven sides.
The join of two angular points is either a side or a diagonal.
The number of lines joining the angular points = 7C2 = \(\frac{7\times6}{1\times}=21.\)
But the number of sides = 7 ∴ The number of diagonals = 21 – 7 = 14.
(ii) Number of diagonals in a polygon of n sides = nC2 – n. Here, n = 20
∴ Required number of diagonals = 20C2 = \(\frac{20\times19}{2\times1}-20=170.\)