• question_answer The number of diagonals of a polygon of 20 sides is A)  $210$            B)  $190$ C)  $180$            D)  $170$

Correct Answer: D

Solution :

Number of diagonals in a polygon of n sides ${{=}^{n}}{{C}_{2}}-n$ Here, $n=20$ $\therefore$ Required number of diagonals ${{=}^{20}}{{C}_{2}}-20$ $=\frac{20\times 19}{2\times 1}-20$ $=170$

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