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A regular polygon has 170 diagonals. Then the measure of interior angle of the polygon is
Options:
Solution:
2842 Upvotes
Verified Answer
The correct answer is:
$\frac{9 \pi}{10}$
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.
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.
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