Question

A soma de dois ˆangulos ´e 140°
. Um deles é
o quadruplo do outro subtraído de 40°
. Determine os dois
ˆangulos (com explicação por favor!)

Answer 1

$\begin{cases}\mathsf{x+y=140^{\circ}}\\\mathsf{y=4x-40^{\circ}}\end{cases}$

$\mathsf{x+4x-40^{\circ}=140^{\circ}}\\\mathsf{5x=140^{\circ}+40^{\circ}}\\\mathsf{5x=180^{\circ}}$

$\mathsf{x=\dfrac{180^{\circ}}{5}}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{x=36^{\circ}}}}}}$

$\mathsf{y=4x-40^{\circ}}\\\mathsf{y=4.36^{\circ}-40^{\circ}}\\\mathsf{y=144^{\circ}-40^{\circ}}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{y=104^{\circ}}}}}}$