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.