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Question
Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.
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Solution
\[\text{ Let n be the number of sides of a polygon } . \]
\[\text { Let x and 5x be the exterior and interior angles } . \]
\[\text{ Since the sum of an interior and the corresponding exterior angle is } 180° , \text{ we have } : \]
\[x + 5x = 180° \]
\[ \Rightarrow 6x = 180° \]
\[ \Rightarrow x = 30° \]
\[\text{ The polygon has n sides } . \]
\[\text{ So, sum of all the exterior angles } = \left( 30n \right)° \]
\[\text{ We know that the sum of all the exterior angles of a polygon is } 360° . \]
\[i . e . , 30n = 360\]
\[ \therefore n = 12\]
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