Math, asked by alkasrivastavapa0eq8, 1 year ago

if number of diagonals of a regular polygon is 27 .then find the interior angles of the polygon

Answers

Answered by sijasubbiah
14
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!

alkasrivastavapa0eq8: thank you friend
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