A regular polygon has 170 diagonals. Then the | vedclass

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(B) The number of diagonals in a polygon with $n$ sides is given by the formula $\frac{n(n-3)}{2}$.Given that the number of diagonals is $170$,we have

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$\frac{9 \pi}{10}$

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(B) The number of diagonals in a polygon with $n$ sides is given by the formula $\frac{n(n-3)}{2}$.Given that the number of diagonals is $170$,we have:$\frac{n(n-3)}{2} = 170$$n(n-3) = 340$$n^2 - 3n - 340 = 0$Solving the quadratic equation using the quadratic formula or factoring:$(n - 20)(n + 17) = 0$Since $n$ must be positive,$n = 20$.The measure of each interior angle of a regular polygon with $n$ sides is given by $\frac{(n-2) \pi}{n}$.For $n = 20$,the interior angle is $\frac{(20-2) \pi}{20} = \frac{18 \pi}{20} = \frac{9 \pi}{10}$.Thus,the correct option is $B$.

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

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