A star-[polygon](https://artofproblemsolving.com/wiki/index.php/Polygon) is drawn on a clock face by drawing a [chord](https://artofproblemsolving.com/wiki/index.php/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](https://artofproblemsolving.com/wiki/index.php/Angle) at each [vertex](https://artofproblemsolving.com/wiki/index.php/Vertex) in the star polygon?
$\mathrm{(A)}\ 20\qquad \mathrm{(B)}\ 24\qquad \mathrm{(C)}\ 30\qquad \mathrm{(D)}\ 36\qquad \mathrm{(E)}\ 60$
[2007 AMC12A-8.png](https://artofproblemsolving.com/wiki/index.php/File:2007_AMC12A-8.png)
We look at the angle between 12, 5, and 10. It subtends $\frac 16$ of the circle, or $60$ degrees (or you can see that the [arc](https://artofproblemsolving.com/wiki/index.php/Arc) is $\frac 23$ of the [right angle](https://artofproblemsolving.com/wiki/index.php/Right_angle)). Thus, the angle at each vertex is an [inscribed angle](https://artofproblemsolving.com/wiki/index.php/Inscribed_angle) subtending $60$ degrees, making the answer $\frac 1260 = 30^{\circ} \Longrightarrow \mathrm{(C)}$