2015 AMC 12B Problem 7

Attempt Problem 7 of the 2015 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

7.

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?
2424
2727
3232
3939
5454
Answer: D
Concepts:regular polygonsymmetry
Small hint:
A regular nn-gon has nn lines of symmetry
Big hint:
Its smallest rotational symmetry angle is 360∘n\dfrac{360^\circ}{n}
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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