The difference between an exterior angle of (n - 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6°. Find the value of n.

Exterior angle of (n - 1) sided regular polygon = $\dfrac{360°}{n - 1}$

Exterior angle of (n + 2) sided regular polygon = $\dfrac{360°}{n + 2}$

Given,

Difference between an exterior angle of (n - 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6°.

$\therefore \dfrac{360°}{n - 1} - \dfrac{360°}{n + 2} = 6° \\[1em] \Rightarrow \dfrac{360°(n + 2) - 360°(n - 1)}{(n - 1)(n + 2)} = 6° \\[1em] \Rightarrow \dfrac{360°.n + 720° - 360°.n + 360°}{n^2 + 2n - n - 2} = 6° \\[1em] \Rightarrow \dfrac{1080°}{n^2 + n - 2} = 6° \\[1em] \Rightarrow 1080° = 6°(n^2 + n - 2) \\[1em] \Rightarrow n^2 + n - 2 = \dfrac{1080°}{6°} \\[1em] \Rightarrow n^2 + n - 2 = 180 \\[1em] \Rightarrow n^2 + n - 2 - 180 = 0 \\[1em] \Rightarrow n^2 + n - 182 = 0 \\[1em] \Rightarrow n^2 + 14n - 13n - 182 = 0 \\[1em] \Rightarrow n(n + 14) - 13(n + 14) = 0 \\[1em] \Rightarrow (n - 13)(n + 14) = 0 \\[1em] \Rightarrow n - 13 = 0 \text{ or } n + 14 = 0 \\[1em] \Rightarrow n = 13 \text{ or } n = -14.$

Since, no. of sides cannot be negative.

∴ n = 13.

Hence, n = 13.