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Question

The number of sides of a regular polygon whose exterior and interior angles are in the ratio 1 : 5 is ___


Solution

Let the number of sides of polygon = n
Each exterior angle =x
Each interior angle =5x
Sum of one interior angle and the corresponding exterior angle is 180
x+5x=180
x=1806=30
Sum of all exterior angles =(360)
If the polygon is regular, then each exterior angle measures 360n.
30×n=360
n=36030
Hence, n = 12.


Mathematics

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