Question

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?

Answer 1

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.