हिंदी

The Sum of the Interior Angles of a Polygon is Three Times the Sum of Its Exterior Angles. Determine the Number of Sided of the Polygon.

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प्रश्न

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sided of the polygon.

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उत्तर

\[\left\{ \left( 2n - 4 \right) \times 90° \right\} = 3 \times \left( \frac{360° }{n} \times n \right)\]

\[ \Rightarrow \left( n - 2 \right) \times 180 = 3 \times 360\]

\[ \Rightarrow n - 2 = 6\]

\[ \therefore n = 8\]

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