Polygon

[MBA]

A certain game board is in the shape of a non-convex polygon, with spokes that extend from each vertex to the center of the board. If each spoke is 8 inches long, and spokes are used nowhere else on the board, what is the sum of the interior angles of the polygon?

(1) The sum of the exterior angles of the polygon is 360º.

(2) The sum of the exterior angles is equal to five times the total length of all of the spokes used.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

I got the answer as C' for this ques, but Manhattan GMAT gives answer as B. Pls clarify?

[JonathanSchneider]

Statement 1 actually doesn't add anything new. Because this is a convex polygon, the sum of the exterior angles MUST equal 360 degrees, by definition. For an explanation of this, check this link: http://www.mathopenref.com/triangleextangle.html

Statement 2, meanwhile, tells us that the total length of all the spokes used = 360/5 = 72. Now, we know that each spoke is 8, so we therefore know that there are 9 total spokes. If there are 9 spokes, we know there are 9 interior angles, and thus 9 sides, which is enough to know the sum of the interior angles, using the formula 180(n-2), where n equals the number of sides.