Q55 / 160 · AP EAMCET 2023 (15 May Shift 1) · Mathematics

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

A
19
Correct answer
B
16
C
13
D
11

Solution

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

Hence, the correct answer is option: 'B'.

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