If there are 9 diagonals in a convex polygon, find the number of sides of the polygon.
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Step by Step Explanation:
- The diagonal of a polygon is the line segment that connects non-adjacent vertices of a polygon.
- Let us consider a polygon with n sides.
We know, the total number of diagonals of a polygon with n sides
- According to the question, the number of diagonals in the convex polygon are 9.
Therefore, 9 =
⇒ 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
- Thus, the given polygon has 6 sides.