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2015 AMC 12B Problem 7

Problem 7 of 25EasierGeometryProblem-Solving Techniques

A regular 1515-gon has LL lines of symmetry, and the smallest positive angle for which it has rotational symmetry is RR degrees. What is L+R?L + R?

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Solution

A regular 1515-gon has L=15L = 15 lines of symmetry, and its smallest angle of rotational symmetry is R=36015=24R = \dfrac{360}{15} = 24 degrees. Then L+R=15+24=39.L + R = 15 + 24 = 39. Thus, the correct answer is D.
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Tagged: regular polygon · symmetry

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