Polygon has 27 diagonals how many sides does it have
Asked by admin @ in Math viewed by 339 People
A polygon has 27 diagonals. How many sides does it have.
Answered by admin @
Let n be the number of vertices of the polygon.
then there are n sides.
N = number of all connections between all the vertices =
N = n(n-1)/2
Number of diagonals = N - n = n (n - 3)/2 = 27 given
n² - 3 n - 54 = 0
(n - 9) (n + 6) = 0
n = 9
so there are 9 sides and 9 vertices
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