a polygon has 20 sides how many diagonals does it have.explin in process
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Answered by
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An n sides polygon has n vertices. If you join every distinct pair of vertices you will get nC2 lines. These nC2 lines account for the n sides of the polygons as well as for the polygons.
So the number of diagonal is given by nC2-n
nC2 - n= n( n-1 ) / 2 - n= n (n-3) / 2
Above is the formula to find the diagonal in case of given sides
So using the formula,
Here given, No of Sides (n) = 20
Now,
No of diagonals= n (n-3) / 2 = 20 (20-3) / 2 = 10 * 17 = 170
Hence, A polygon which has 20 sides have 170 diagonals.
So the number of diagonal is given by nC2-n
nC2 - n= n( n-1 ) / 2 - n= n (n-3) / 2
Above is the formula to find the diagonal in case of given sides
So using the formula,
Here given, No of Sides (n) = 20
Now,
No of diagonals= n (n-3) / 2 = 20 (20-3) / 2 = 10 * 17 = 170
Hence, A polygon which has 20 sides have 170 diagonals.
Answered by
0
Answer:
17 diagonals
Step-by-step explanation:
n(n-3)/2 by this method we do
I hope It may help you
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