Problem:
A regular 15 -gon has lines of symmetry, and the smallest positive angle for which it has rotational symmetry is degrees. What is ?
Answer Choices:
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Solution:
The lines of symmetry are the 15 lines joining a vertex to the midpoint of the opposite side, so . There is rotational symmetry around the center of the 15-gon, and the smallest positive angle of rotation that will transform the 15 -gon onto itself is degrees; therefore . The sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions