Hi Anaira Mitch,
This question can be solved with 'brute force', although you do have to know a few math/geometry rules to get to the correct answer.
To start, when it comes to polygons, another way to think about the total of the angles in the polygon is: "add a side, add 180 degrees"...
For example:
3-sided shape = 180 degrees
4-sided shape = 360 degrees
5-sided shape = 540 degrees
6-sided shape = 720 degrees
7-sided shape = 900 degrees
Etc.
Here, we're told that a polygon with an unknown number of sides has angles that are CONSECUTIVE INTEGERS and that the MEDIAN of those angles = 140 degrees.
Since we're dealing with consecutive integers, the median angle of the polygon can only be one of two options: an integer (if there are an ODD number of sides) or a non-integer (a number that ends in .5.... if there are an EVEN number of sides). Since the median here is 140, there MUST be an ODD number of sides.
From here, we can brute-force the possibilities until we find the one that fits all of the given information. Keep in mind that we need the sum of the angles to be the proper MULTIPLE of 180...
3-sided shape: 139, 140, 141 - This is clearly not a possible triangle.
5-sided shape: 138, 139, 140, 141, 142 - This totals 700 degrees, which doesn't "match" (a 5-sided shape has 540 degrees)
7-sided shape: 137, 138, 139, 140, 141, 142, 143 - This totals 980 degrees, which doesn't "match" (a 7-sided shape has 900 degrees)
9-sided shape: 136, 137, 138, 139, 140, 141, 142, 143, 144 - This totals 1260 degrees, which DOES "match" (a 7-sided shape has 1260 degrees)
Thus, we're dealing with a 9-sided polygon and the smallest angle is 136 degrees.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
