MathDB

An "n-pointed star" is formed as follows: the sides of a convex polygon are numbered consecutively

1,2,\cdots,k,\cdots,n

n\geq 5

; for all

n

values of

k

, sides

k

and

k+2

are non-parallel, sides

n+1

and

n+2

being respectively identical with sides

1

and

2

; prolong the

n

pairs of sides numbered

k

and

k+2

until they meet. (A figure is shown for the case

n=5

) http://www.artofproblemsolving.com/Forum/album_pic.php?pic_id=704&sid=8da93909c5939e037aa99c429b2d157a Let

S

be the degree-sum of the interior angles at the

n

points of the star; then

S

equals:

\text{(A)} \ 180 \qquad \text{(B)} \ 360 \qquad \text{(C)} \ 180(n+2) \qquad \text{(D)} \ 180(n-2) \qquad \text{(E)} \ 180(n-4)

Problem Statement