Question

Na figura a seguir, I é o ponto de encontro das duas bissetrizes do triângulo ABC. Qual é a medida, em graus, de x?

Answer 1

Resposta:

Explicação passo-a-passo:

$\hat{ABC} = 20\textdegree\\\hat{BAC} = 110\textdegree\\\hat{ACB}+\hat{ABC}+\hat{BAC} = 180\textdegree\\\hat{ACB} + 20\textdegree + 110\textdegree = 180\textdegree\\\hat{ACB} = 50\textdegree\\\\\hat{BCI} = \frac{\hat{ACB}}{2} = 25\textdegree\\ \hat{BIC} + \hat{IBC}+\hat{BCI} = 180\textdegree\\\hat{BIC} + 10\textdegree + 25\textdegree = 180\textdegree\\\hat{BIC} = 145\textdegree\\x+\hat{BIC} = 180\textdegree\\ x = 180\textdegree - 145\textdegree = 35\textdegree$