2015 AMC 12B Problem 7

Below is the professionally curated solution for Problem 7 of the 2015 AMC 12B, 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 of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:regular polygonsymmetry

Difficulty rating: 1260

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

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.

Problem 7 in Other Years