Question

A polygon has 90 diagonals. Find the number of its sides?​

Answer 1

Answer:

Solution:

Let, number of sides = n, number of vertex = n, number of lines = nC2

Number of diagonals = nC2 – n = n(n-3)/2

90 = n(n-3)/2

n2 -3n = 180

n2 – 3n – 180 = 0

Solving for n, we get;

n = 15, -12

Number of sides cannot be negative. Therefore,

n = 15 is the answer.

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