The exterior angle of a regular polygon is $20^\circ$.  

1. What is the measure of an interior angle of this polygon? Show how you know.

   Hint (a):

   The interior and exterior angles are supplementary.

   

2. How many sides does this polygon have? Show all work.

   Hint (b):

   The sum of the measures of the exterior angles is $360^\circ$.

   Answer (b):

   $18$