A Star Polygon
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?(in degrees)
The answer is 30.
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1 solution
We look at the angle between 12, 5, and 10. It subtends 1/6 of the circle, or 60 degrees (or you can see that the arc is 2/3 of the right angle). Thus, the angle at each vertex is an inscribed angle subtending 60 degrees, making the answer0.5*60 = 30