Question

se ABC é um triângul, o valor de a é?

a) 10
b) 15
c) 20
d) 25

Answer 1

Vamos achar o ângulo ABC, sabendo que a soma dos ângulos internos de um triângulo é 180º:

$A\^BC+B\^AE+B\^EA=180\º\\\\A\^BC+\alpha+70\º=180\º\\\\A\^BC+\alpha=180\º-70\º\\\\A\^BC+\alpha=110\º\\\\\boxed{\boxed{A\^BC=110\º-\alpha}}$

Agora, fazendo o mesmo no triângulo ABC:

$A\^BC+B\^AC+B\^CA=180\º\\\\(110\º-\alpha)+(\alpha+\alpha+\alpha)+40\º=180\º\\\\110\º-\alpha+3\alpha+40\º=180\º\\\\2\alpha+150\º=180\º\\\\2\alpha=180\º-150\º\\\\2\alpha=30\º~~~~~\Longrightarrow~~~~~\boxed{\boxed{\alpha=15\º}}$