if number of diagonals of a regular polygon is 27 .then find the interior angles of the polygon
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Hey
Here is your answer,
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
Angle = 360°/9
=40°
Hope it helps you!
Here is your answer,
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
Angle = 360°/9
=40°
Hope it helps you!
alkasrivastavapa0eq8:
thank you friend
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