Seção II: Ângulos ⇒ Problema 109 - Linhas Retas e Ângulos-Vol. 1 Tópico resolvido

[petrasMOD]

São dados os ângulos consecutivos AOB, BOC e COD tal que:
[tex3]7m\angle AOC =5m\angle COD\\
5m\angle BOD -7m\angle AOB = 120^o [/tex3]
Calcular [tex3]m\angle BOC[/tex3]

Resposta

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Gabarito: B) 10^o

[rcompany]

[tex3]m\angle AOB=a,m\,\angle BOC=b,\,m\angle COD=c\\\\
\begin{array}{rl}\left.\begin{array}{rl}7m\angle AOC =5m\angle COD\\
5m\angle BOD -7m\angle AOB = 120°\end{array}\right\}
&\implies
\left\{\begin{array}{l}7(a+b)=5c\\
5(b+c)-7a = 120°\end{array}\right.\\
&\implies
\left\{\begin{array}{l}7a=5c-7b\\
7a = 5b+5c-120°\end{array}\right.\\
&\implies 5c-7b=5b+5c-120\\&\implies 12b=120°\\&\implies b=10°\end{array}\\
\fbox{$\quad\angle BOC=10°\quad$}[/tex3]