Question

Calcule a soma dos ângulos abaixo

Answer 1

A soma dos ângulos internos do triangulo deve valer 180°, logo:

$a+b+90^\circ~=~180^\circ\\\\\\a+b~=~180^\circ-90^\circ\\\\\\\boxed{a+b~=~90^\circ}\\\\\\\\c+d+90^\circ~=~180^\circ\\\\\\c+d~=~180^\circ-90^\circ\\\\\\\boxed{c+d~=~90^\circ}\\\\\\\\e+f+90^\circ~=~180^\circ\\\\\\e+f~=~180^\circ-90^\circ\\\\\\\boxed{e+f~=~90^\circ}\\\\\\\\g+h+90^\circ~=~180^\circ\\\\\\g+h~=~180^\circ-90^\circ\\\\\\\boxed{g+h~=~90^\circ}$

Sendo assim, a soma dos ângulos vale:

$(a+b)~+~(c+d)~+~(e+f)~+~(g+h)~=\\\\\\=~(90^\circ)~+~(90^\circ)~+~(90^\circ)~+~(90^\circ)\\\\\\=~\boxed{360^\circ}$