Question Number 196320 by sniper237 last updated on 22/Aug/23
$$\:\:{If}\:\:{a}\:\:{regular}\:{n}−{polygon}\:{can} \\ $$$$\:{be}\:{divided}\:{into}\:\:{n}\:\:{identical}\:\: \\ $$$${equilateral}\:{triangles}\:{then}\:\:{n}=\mathrm{6} \\ $$
Answered by Rasheed.Sindhi last updated on 23/Aug/23
$${n}−{polygon}\:{consists}\:{n}\:\boldsymbol{{equilateral}}\:\boldsymbol{{triangles}} \\ $$$$\therefore\:{Central}\:{angle}\:=\mathrm{60} \\ $$$$\:\:\:\:{Central}\:{angle}\:=\:\:\frac{\mathrm{360}}{{n}}=\mathrm{60}\Rightarrow{n}=\mathrm{6} \\ $$