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Question

If a polygon has 90 diagonals, the number of its sides is given by?


A

12

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B

11

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C

10

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D

15

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Solution

The correct option is D

15


Explanation for the correct option:

Find the number of sides of the polygon :

Let, number of sides =n, number of vertex =n, number of lines =C2n

Number of diagonals =C2nn=n(n-3)2

90=n(n-3)2n2-3n=180n23n180=0

Solving for n, we get;

n2-15n+12n-180=0(n-15)(n+12)=0

n=15,-12

The number of sides cannot be negative. Therefore, n=15.

Hence the correct option is D.


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