AP EAMCET · Maths · Permutation Combination
A regular polygon has 170 diagonals. Then the measure of interior angle of the polygon is
- A \(\frac{5 \pi}{8}\)
- B \(\frac{9 \pi}{10}\)
- C \(\frac{7 \pi}{10}\)
- D \(\frac{17 \pi}{20}\)
Answer & Solution
Correct Answer
(B) \(\frac{9 \pi}{10}\)
Step-by-step Solution
Detailed explanation
Given, Number of diagonals in a polygon \(=170\) \[ \begin{aligned} \frac{n(n-3)}{2} & =170 \\ n(n-3) & =340 \\ n(n-3) & =20 \times 17 \\ \therefore \quad n & =20 \end{aligned} \] \(\therefore\) Measure of interior angle…
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