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Q.

If the ratio between exterior angle and interior angle of a regular polygon is 1:5. Then the number of sides of the polygon is ____.


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Detailed Solution

If the ratio between exterior angle and interior angle of a regular polygon is 1:5. Then the number of sides of the polygon is 12.
Given that, the ratio between exterior angle and interior angle of a regular polygon is 1:5.
Assuming the interior angle be 5x and the exterior angle be x.
As we know exterior angle = 180° - interior angle. So,
x = 180° − 5x x + 5x = 180° 6x = 180° x = 180°/6 x = 30°  
So, each exterior angle= 30°.
Now, we have the number of sides = 360 ° exterio r angle  
=360∘30∘
=363
=12
Hence, the number of sides of the polygon is 12.
 
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