Question

as retas A e B são concorrentes. obtenha o valor de x dos ângulos assinalados

Answer 1

1)

Os ângulos "3x+13°" e "x+45°" são opostos pelo vértice e, portanto iguais, logo:

$3x+13^\circ~=~x+45^\circ\\\\\\3x-x~=~45^\circ-13^\circ\\\\\\2x~=~32^\circ\\\\\\x~=~\frac{32^\circ}{2}\\\\\\\boxed{x~=~16^\circ}$

2)

Os ângulos "3x-12°" e "2x-5°" são opostos pelo vértice e, portanto iguais, logo:

$3x-12^\circ~=~2x-5^\circ\\\\\\3x-2x~=\,-5^\circ+12^\circ\\\\\\\boxed{x~=~7^\circ}$