A regular polygon has 170 diagonals. Then the measure of interior angle of the polygon is

A regular polygon has 170 diagonals. Then the measure of interior angle of the polygon is
  1. $\frac{5 \pi}{8}$
  2. $\frac{9 \pi}{10}$
  3. $\frac{7 \pi}{10}$
  4. $\frac{17 \pi}{20}$

Solution

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 $=\frac{(n-2) \pi}{n}=\frac{18 \pi}{20}=\frac{9 \pi}{10}$ Hence, option (2) is correct

Asked in: AP EAMCET 2020 (22 Sep Shift 2)

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