Question

Is the sum of the interior angles of a convex polygon the same as a non-convex (concave) polygon?

Answer 1

Yes.
Sum of Interior Angles
The interior angles of any polygon always add up to a constant value, which depends only on the number of sides. For example the interior angles of a pentagon always add up to 540° no matter if it regular or irregular, convex or concave, or what size and shape it is. (I was unsure on that myself - glad you asked.)
http://www.mathopenref.com/polygoninteriorangles.html