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Q.

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5.


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a

10

b

12

c

14

d

15 

answer is B.

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Detailed Solution

Ratio of external and internal angles = 1:5
Let, exterior angle be = 1x
interior angle be = 5x
Now, 1x + 5x = 180
or, 6x = 180
or, x = 30
So exterior angle = 1x = 1×30 = 30°
interior angle = 5x = 5×30 = 150°

No. of sides of polygon = 360exterior angle
=36030=12
So, the polygon is of 12 sides.
Hence (2) is the correct answer.
 
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