TS EAMCET · Maths · Permutation Combination
A regular polygon of \(n\) sides has 170 diagonals, then \(n\) is equal to
- A \(12\)
- B \(17\)
- C \(20\)
- D \(25\)
Answer & Solution
Correct Answer
(C) \(20\)
Step-by-step Solution
Detailed explanation
We know that, \(\begin{array}{rlrl}\text { Number of diagonals } & =\frac{n(n-3)}{2} \\ & \therefore & 170 & =\frac{n(n-3)}{2} \\ \Rightarrow & 340 & =n(n-3) \\ \Rightarrow & 20 \times 17 & =n(n-3) \\ \Rightarrow & n & =20\end{array}\)
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