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Question
The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in the polygon.
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Solution
Let exterior angle = x° & interior angle = 4x°
∴ 4x + x = 180°
5x = 180°
x = 36°
∴ Each exterior angle = 36°
Let no.of sides = n
∴ `360^circ/"n" = 36^circ`
n = `360^circ/36^circ`
n = 10
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