[tex]\displaystyle \sf \text{N\'umeros de diagonais de um pol\'igono } : \\\\ D = \frac{n\cdot (n-3)}{2} \\\\\ temos : \\\\ \frac{n\cdot (n-3)}{2}+105 = \frac{(n+7-3)\cdot (n+7)}{2} \\\\\ \frac{n\cdot (n-3)+210}{2}= \frac{(n+4)\cdot (n+7)}{2} \\\\\\ n^2-3n+210 = n^2+7n+4n+28 \\\\ 11n+3n =210-28 \\\\ 14n = 182 \\\\ n=\frac{182}{14} \\\\\\\ \large\boxed{\sf \ n=13\ }\checkmark[/tex]
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[tex]\displaystyle \sf \text{N\'umeros de diagonais de um pol\'igono } : \\\\ D = \frac{n\cdot (n-3)}{2} \\\\\ temos : \\\\ \frac{n\cdot (n-3)}{2}+105 = \frac{(n+7-3)\cdot (n+7)}{2} \\\\\ \frac{n\cdot (n-3)+210}{2}= \frac{(n+4)\cdot (n+7)}{2} \\\\\\ n^2-3n+210 = n^2+7n+4n+28 \\\\ 11n+3n =210-28 \\\\ 14n = 182 \\\\ n=\frac{182}{14} \\\\\\\ \large\boxed{\sf \ n=13\ }\checkmark[/tex]