**(i) **a hexagon

We know that a hexagon has 6 angular points. By joining those any two angular points we get a line which is either a side or a diagonal.

So number of lines formed = ^{6}C_{2}

By using the formula,

^{n}C_{r} = \( \dfrac{ n!}{r!(n – r)!}\)

^{6}C_{2} =\( \dfrac{6!}{2!(6-2)!}\)

=\(\dfrac{ 6×5 }{ (2×1)}\)

= 3×5

= 15

We know number of sides of hexagon is 6

So, number of diagonals = 15 – 6 = 9

The total no. of diagonals formed is 9.

**(ii) **a polygon of 16 sides

We know that a polygon of 16 sides has 16 angular points. By joining those any two angular points we get a line which is either a side or a diagonal.

So number of lines formed = ^{16}C_{2}

By using the formula,

^{n}C_{r} =\( \dfrac{ n!}{r!(n – r)!}\)

^{16}C_{2} = \(\dfrac{ 16!}{2!(16-2)!}\)

= \(\dfrac{ 16×15 }{ (2×1)}\)

= 8×15

= 120

We know number of sides of a polygon is 16

So, number of diagonals = 120 – 16 = 104

The total no. of diagonals formed is 104.

Answered by Sakshi | 1 year agoHow many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

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