Triângulos - 2008 - Vol. 2 ⇒ 019 - Triângulos - 2008 Tópico resolvido

[petrasMOD]

Na figura mostrada, calcular o valor de x, se m + n = 220º

Resposta

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35^o

[petrasMOD]

[tex3]\mathsf{\triangle EFM:180-(\alpha+\beta)+180-(\theta+\phi) +x = 180 \implies x = \alpha+\phi+\beta+\theta-180^o\\
ABCD:2\alpha+2\phi +220 = 360 \implies \alpha+\phi=70^o \\
\triangle MGH:x+\beta+\theta =180^o \implies \beta+\theta = 180^o -x\\
Substituindo: x = 70+180-x-180 \implies 2x = 70\\
\therefore \boxed{x = 35^o}
}
[/tex3]