Problem:
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 . What is the degree measure of the angle at each vertex in the star-polygon?
Answer Choices:
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Solution:
Consider the two chords with an endpoint at 5. The arc subtended by the angle determined by these chords extends from 10 to 12 , so the degree measure of the arc is . By the Central Angle Theorem, the degree measure of this angle is . By symmetry, the degree measure of the angle at each vertex is .
The problems on this page are the property of the MAA's American Mathematics Competitions