If there are 9 diagonals in a convex polygon, find the number of sides of the polygon.


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Answer:

6

Step by Step Explanation:
  1. The diagonal of a polygon is the line segment that connects non-adjacent vertices of a polygon.
  2. Let us consider a polygon with n sides.
    We know, the total number of diagonals of a polygon with n sides =  
    n(n - 3)
    2
     
  3. According to the question, the number of diagonals in the convex polygon are 9.
    Therefore, 9 =  
    n(n - 3)
    2
     
    ⇒ 18 = n2 - 3n
    ⇒ n2 - 3n - 18 = 0
    ⇒ (n - 6)(n + 3) = 0
    Either, (n - 6) = 0 or (n + 3) = 0
    Since, a polygon never have 0 or less than zero sides,
    and hence, (n + 3) ≠ 0.
    Therefore, (n - 6) = 0
    ⇒ n = 6
  4. Thus, the given polygon has 6 sides.

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