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  • In a 20-sided polygon, how many diagonals are there?  Option: 1 200Option: 2</

In a 20-sided polygon, how many diagonals are there?

 

Option: 1

200


Option: 2

170


Option: 3

160


Option: 4

150


Answers (1)

best_answer

Given that,

There are 20 sides in a polygon.

Two non-adjacent vertices can be joined to create a diagonal.

The number of diagonals of a 20-sided polygon = The number of line segments in a 20-sided polygon – 12 edges of the polygon.

Thus,

\mathrm{\begin{aligned} & N={ }^{20} C_2-20 \\ & N=\frac{20 !}{2 ! 18 !}-20 \\ & N=\frac{20 \times 19}{2}-20 \\ & N=190-20 \\ & N=170 \end{aligned}}

Therefore, the total number of diagonals formed is 170.

Posted by

shivangi.bhatnagar

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