Number of equilateral triangles formed by the vertices of a regular polygon of n sides 
 

$$\begin{gathered} \text{number of equilateral triangles by joining vertices} \\ \text{ =}\frac{\text{ the number of sides in polygon}}{3} \\ \text{it's true if the number of sides is multiple by 3 .} \\ \mathrm{Consider} \mathrm{that} \mathrm{vertices} \mathrm{of} \mathrm{a} \mathrm{equilateral} \mathrm{triangle} \\ , \mathrm{if} \mathrm{you} \mathrm{fix} \mathrm{one} \mathrm{vertex}, \mathrm{the} \mathrm{next} \mathrm{one} \mathrm{would} \mathrm{be} \mathrm{an} \mathrm{angle} \mathrm{of} 2\mathrm{\pi }/3 \mathrm{after} \mathrm{it} \end{gathered}$$