Seção II: Ângulos ⇒ Problema 111 - Linhas Retas e Ângulos-Vol. 1 Tópico resolvido

[petrasMOD]

Dado os ângulos consecutivos AON, NOM e MOB tal que:
[tex3]m\angle AOB = 90^o [/tex3] e [tex3]m\angle AOM+ m\angle NOB = 140^o[/tex3].
Calcular [tex3]m\angle MON.[/tex3]

Resposta

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Gabarito: C) 50^o

[petrasMOD]

[tex3]m\angle AON + m\angle NOM + m\angle MOB = m\angle AOB\\
m\angle AON + m\angle NOM + m\angle MOB = 90^\circ (Eq. 1)\\
m\angle AOM + m\angle NOB = 140^\circ\\
(m\angle AON + m\angle NOM) + (m\angle NOM + m\angle MOB) = 140^\circ\\
[/tex3][tex3]m\angle AON + m\angle NOM + m\angle MOB) + m\angle NOM = 140^\circ(Eq.2)[/tex3]
Substituíndo Eq. 1 na Eq. 2:
[tex3]90^\circ + m\angle NOM = 140^\circ\\
m\angle NOM = 140^\circ - 90^\circ\\
\boxed{m\angle NOM = 50^\circ}
[/tex3]