✅ Ângulos opostos pelo vértice:
Sejam os ângulos:
[tex]\large\displaystyle\text{$\begin{gathered}\alpha = 5x - 10\\\beta = 4x + 4 \end{gathered}$}[/tex]
Se este ângulos são opostos pelo vértice, então significa que as medidas desses ângulos são iguais: Então:
[tex]\large\displaystyle\text{$\begin{gathered}\alpha = \beta \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}5x - 10 = 4x + 4 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}5x - 4x = 4 + 10 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}x = 14 \end{gathered}$}[/tex]
Agora podemos calcular o valor dos ângulos. Então:
[tex]\large\displaystyle\text{$\begin{gathered}\alpha = \beta \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}5\cdot14 - 10 = 4\cdot14 + 4 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}70 - 10 = 56 + 4 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}60 = 60 \end{gathered}$}[/tex]
✅ Portanto:
[tex]\large\displaystyle\text{$\begin{gathered}\alpha = \beta = 60^o \end{gathered}$}[/tex]
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