Hi, 

*Note: Polygon with n sides has n(n-3)/2 diagonals. for ex, rectangle has 2 diagonals

polygon with 44 diagonals:

44 = n(n-3)/2

solving for n

n^2-3n -88 = 0

factoring

(n-11)(n+8) = 0

(n+8) = 0

n = -8 cannot use this

(n-11)=0

n = 11

Polygon has 11 sides



checking our answer

11*8/2 = 44 diagonals





 

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