2015 AMC 12B Problem 7 — Solution | LIVE by Po-Shen Loh

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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 $15$ -gon has $L$ lines of symmetry, and the smallest positive angle for which it has rotational symmetry is $R$ degrees. What is $L + R?$

$24$

$27$

$32$

$39$

$54$

Answer: D

Concepts:regular polygon symmetry

Difficulty rating: 1260

Solution:

A regular $15$ -gon has $L = 15$ lines of symmetry, and its smallest angle of rotational symmetry is $R = \dfrac{360}{15} = 24$ degrees.

Then $L + R = 15 + 24 = 39.$

Thus, the correct answer is D.

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