If the ratio of an external angle and an internal angle of a regular polygon is 1 : 5, then what is the number of sides in the polygon?

If the ratio of an external angle and an internal angle of a regular polygon is 1 : 5.

Let's assume the external angle and an internal angle of a regular polygon are 'y' and '5y' respectively.

As we know that the sum of the external and internal angles of a regular polygon is 180$$^{\circ\ }$$

the external angle of a regular polygon = $$\frac{180^{\circ\ }\ }{1+5}\times1$$

= $$\frac{180^{\circ\ }\ }{6}\times1$$

= $$30^{\circ\ }$$

Number of sides in the polygon = $$\frac{360^{\circ\ }}{external\ angle\ of\ a\ regular\ polygon}$$

= $$\frac{360^{\circ\ }}{30^{\circ\ }}$$

= 12