It is good to remember that a polygon with n sides has nC2 - n diagonals and follow up from there as Bunuel did or follow shrouded1's approach, which I thought was pretty cool too.
Though, remember that if you are lost with the 21 sides, cannot think of the formula and are hard pressed for time, try and work it on a smaller scale.
Lets see what happens in a 6 sided figure which is extremely easy to draw:
6 sided figure. 1 vertex left alone. When you start from the first point, you cant join it to 3 of the 6 points - itself, point left alone and point next to it.
Total diagonals drawn: 3 + 2 + 1
Ques.jpg [ 18.05 KiB | Viewed 2398 times ]
21 sided figure. When you will start with the first point, you will not join it to 3 of the 21 points - itself, point left alone and point next to it.
Total diagonals drawn will be: 18 + 17 + 16 + ... +1 = 18*19/2 = 171
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