AMC 12 2007a Problem 8

A star-polygon is drawn on a clock face by drawing a chord from each number to the fifth number counted clockwise from that number. That is, chords are drawn from 12 to 5, from 5 to 10, from 10 to 3, and so on, ending back at 12. What is the degree measure of the angle at each vertex in the star polygon?

$\mathrm{(A)}\ 20 \mathrm{(B)}\ 24 \mathrm{(C)}\ 30 \mathrm{(D)}\ 36 \mathrm{(E)}\ 60$