The measures of the interior angles in a polygon are consecutive integers. the smallest angle measures 136 degrees. how many sides does this polygon have?

Other than writing an iterative computer program to determine this answer, it can be done manually.

Using N as the number of sides of a polygon, (N-2) 180 = number of degrees of an N-sided polygon. The range from 180 up to 1260 for a 9 sided polygon.

Starting with 136 and adding consecutive numbers to it, the answer turns out to be a 9 sided polygon of 1260 degrees.