Let $X$ be a regular $n$-gon with vertices $A_1, A_2, \cdots, A_n$ for $n \gt 6$. Suppose the sides $A_1 A_2$ and $A_5 A_4$ are extended externally to meet at a point $P$, outside $X$. If $\angle A_2 P A_4=\frac{2 \pi}{3}$, the value of $n$ is

• A

  $12$
• B

  $20$
• C

  $24$
• Correct answer
  D

  $18$

Hence, the correct answer is option: 'D'.