Question

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

Answer 1

The sum of  one exterior angle and one interior angle is 180°  since they form a linear pair. Let the exterior angle be x
angles are in ratio 1:5  ; so, the  angle is 5x 
Now
x + 5x = 180°
6x = 180°

x = 30°...the exterior angle is equal to 30°.

The sum of the exterior angles of a regular polygon is 360°.
So,we multiply the exterior angle by the number of the sides. 
n.x =360° , where 'n' is the no. of sides
n.30 = 360°
n = 360/30 = 12


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