AMC12 2015 B

AMC12 2015 B · Q7

AMC12 2015 B · Q7. It mainly tests Symmetry.

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 $L+R$?

一个正15边形有$L$条对称轴，其最小的正旋转对称角是$R$度。求$L+R$。

(A) 24 24

(B) 27 27

(D) 39 39

(E) 54 54

Answer

Correct choice: (D)

正确答案：（D）

Solution

A regular 15-gon (odd number of sides) has 15 lines of symmetry, each from a vertex to the midpoint of the opposite side, so $L=15$. The smallest positive rotational symmetry about the center is $\frac{360}{15}=24^\circ$, so $R=24$. Thus $L+R=39$.

正15边形（边数为奇数）有15条对称轴，每条从一个顶点到对边中点，因此$L=15$。中心的最小正旋转对称角为$\frac{360}{15}=24^\circ$，因此$R=24$。故$L+R=39$。

Topics

GE.012 Symmetry