The ratio of interior angle : exterior angle of a regular polygon is 5 : 1.
Calculate the number of sides that the polygon has. Answer ... sides

1. Find the size of one exterior angle using the given ratio.

Interior angle : exterior angle $=5:1$.

Let the interior angle be $5x$ and the exterior angle be $x$.

Since they are supplementary,
$5x+x=180^\circ$
$6x=180^\circ$
$x=30^\circ$

So each exterior angle is $30^\circ$.

2. Use the exterior angle to find the number of sides.

For a regular polygon,
$\text{number of sides}=\frac{360^\circ}{\text{exterior angle}}$
$n=\frac{360^\circ}{30^\circ}=12$