2015 AMC 12B 第 7 题

Question

一个正

15

边形有

L

条对称轴，并且使它具有旋转对称性的最小正角为

R

度。

L + R

是多少？

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

一个正

n

边形有

n

条对称轴

A regular

n

-gon has

n

lines of symmetry

它的最小旋转对称角是

\dfrac{360^\circ}{n}

。

Its smallest rotational symmetry angle is

\dfrac{360^\circ}{n}

一个正

15

边形有

L = 15

条对称轴，它的最小旋转对称角是

R = \dfrac{360}{15} = 24

度。

于是

L + R = 15 + 24 = 39

。

因此，正确选项是 D。

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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