goi \(\frac{180\left(n-2\right)}{n}\)la so do cua mot da giac deu co n canh
goi \(\frac{180\left(m-2\right)}{m}\) la so do cua mot da giac deu co m canh
theo bai ra, ta co: \(\frac{\frac{180\left(n-2\right)}{n}}{\frac{180\left(m-2\right)}{m}}=\frac{5}{7}\)\(\Leftrightarrow\frac{180\left(n-2\right)}{n}.\frac{m}{180\left(m-2\right)}=\frac{5}{7}\)
\(\Leftrightarrow\frac{\left(n-2\right)m}{n\left(m-2\right)}=\frac{5}{7}\)\(\Leftrightarrow5mn-10n-7mn+14m=0\)
\(\Leftrightarrow\)-2mn-10n+14m=0\(\Leftrightarrow\)-2n(m+5)+14(m+5)=70
\(\Leftrightarrow\)(m+5)(7-n)=35=\(\pm1.\pm35=\pm5.\pm7\)
roi sau do ban tu giai nha.ket qua la n=6