CAT 2016 Quantitative Ability

Question : 29 of 34

Marks: +1, -0

In a regular polygon, the number of diagonals is 'k' times the number of sides. If the interior angle of the polygon is 0, then the value of k is

Solution:

Interior angle of an n-sided regular polygon

=\;\;{(n-2)π}/{n}=θ

⇒

n=\;\;{2π}/{π-θ}

The number of diagonals in an n-sided polygon

=^{n}C_{2}-n=kn

⇒

\;\;{n(n-3)}/{2}=kn

Hence

k=\;\;{(\;\;{2π}/{π-θ})-3}/{2}=\;\;{3θ-π}/{2(π-θ)}

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