Math, asked by Vovo, 1 year ago

COULD SOMEONE PLEASE ANSWER THIS?! Pleeeeaaaaase??!!!
IT'S ABT ANGLE PROPERTIES BTW
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When x and y are integers, find their respective values when an n-sided polygon has a total of  \frac{1}{x} n(n-y) diagonals.

Answers

Answered by Kkashyap
1
We know that polygon of n-sides has

n(n-3)/2 diagonals.

So,1/x n(n-y)=1/2 n( n-3)

Equating both we get

x=2 and y=3

Hope it helps

Vovo: Oh. But then...how do I answer the question when that formula you've mentioned[n(n-3)/2] isn't given? Like, they gave some data: a polygon w/ 3 sides has 0 diagonals, 4 sides, 2 diagonals and so on...
Vovo: Maybye I should have phrased this better...
Kkashyap: With polygon of three sides , diagonals=0.It means if there is some value on subtraction which is equal to no. Of sides here i.e 3. So,from this we get one part of formula (n-3).Now for 4-sided polygon no of diagonals=2 but (n-3)=(4-3)=1,so,from here we derive another multiplying factor which is 2 ,in terms of side it is =4/2.=n/2. i.e new formula =n(n-3)/2
Kkashyap: Also, polygon with 5-sideshas 5 diagonal , putting n=5 in previous formula we get no. Of diagonals=5. Hence, formula verified
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