If $3-$gon and $5-$gon are constructible, show that $15-$gon is too. > Use the fact that the regular $3-$gon and the regular $5-$gon are constructible to show that the regular $15-$gon is constructible. What is the best way to prove this? I have found a theorem that states that if $gcd(m,n)=1$ where $n-$gon and $m-$gon constructible, then the $mn-$ is also constructible. Is there a better way to prove the question above?

Sure, if you can construct a regular 3-gon and a regular 5-gon, that means you can construct angles of 120° and 72°, which means you can construct the angle of $2\cdot 72° - 120°$, which is 24°, and that is all it takes to construct a regular 15-gon.