Question

Conside um poligono regular cuja soma dos ângulos internos é 3 240. A Medida de cada ângulo interno desse poligono é ( A) 147,27 ( B ) 162 ( C ) 180 (D) 202,5

Answer 1

$\mathsf{S_{i}=(n-2)\cdot\,180^{\circ}}\\\mathsf{(n-2)\cdot\,180^{\circ}=3240^{\circ}}\\\mathsf{n-2=\dfrac{3240^{\circ}}{180^{\circ}}}\\\mathsf{n-2=18}\\\mathsf{n=18+2}\\\mathsf{n=20}$

$\mathsf{a_{i}=\dfrac{S_{i}}{n}}\\\mathsf{a_{i}=\dfrac{3240^{\circ}}{20}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{n=162^{\circ}}}}}}$