Question

qual é o poligono regular M que ai-ae=100, sendo ai, a medida do angulo interno e ae a medida do angulo externo?

Answer 1

$\mathrm{A_i-A_e=100\ \to\ \dfrac{(n-2).180}{n}-\dfrac{360}{n}=100}\\\\ \mathrm{\dfrac{(n-2).18-36}{n}=10\ \to\ 18\big((n-2)-2\big)=10n}\\\\ \mathrm{9(n-4)=5n\ \to\ 9n-36=5n\ \to\ 9n-5n=36}\\\\ \mathrm{4n=36\ \to\ n=\dfrac{36}{4}\ \to\ \boxed{\mathbf{n=9}}}\\\\ \textbf{Resposta:}\ \mathrm{o\ pol\'igono\ M\ \'e\ o\ ene\'agono.}$