If the number of diagonals of a regular polygon of $n$ sides is 104 , then $\mathrm{n}=$

If the number of diagonals of a regular polygon of $n$ sides is 104 , then $\mathrm{n}=$
  1. 19
  2. 16
  3. 13
  4. 11

Solution

We know that, Number of diagonals of a regular $ \begin{aligned} & \text { polygon of } n \text { sides }=\frac{(n-3) n}{2} \\ & \Rightarrow \quad 104=\frac{(n-3) n}{2} \\ & \Rightarrow \quad n=16 \text { and } n=-13 \text { (Rejected) } \\ & \Rightarrow \quad n=16 \end{aligned} $

Asked in: AP EAMCET 2023 (15 May Shift 1)

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