If the measure of one interior angle of a regular polygon is 156 degrees, how many sides does it have? can a regular polygon have and interior angle of 157 degrees? explain your answer

One exterior angle = 180 - 156 = 24 degrees
Recall that the sum of all the exterior angles of a polygon add up to 360 degrees.
So the number of sides in this polygon = number of exterior angles = 360 / 24
=  15 

If interior angles was 157 , exterior one = 23 degrees
360 / 23 does not divide to give an integer 

so a regular polygon cannot have an interior angle of 157.

The first one is 2/3the second is 1/160the third is 4/125