Triângulos - 2008 - Vol. 2 ⇒ 006 - Triângulos - 2008 Tópico resolvido

[petrasMOD]

Do gráfico mostrado calcular "x"

Resposta

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Gabarito: 65^o

[petrasMOD]

[tex3]\mathsf{
180-2\theta + 180-2\phi+80 = 180 \implies \theta+\phi = 130^o \\
\underbrace{\theta +\phi} +2\beta+2\delta =360^o \implies 130+2(\beta+\delta) = 360^o
\\ \therefore \beta + \delta = 115^o \\
\triangle_{central}> x+180-(\theta+\beta) +180-(\phi+\delta) = 180\\
x-(\theta+\beta+\phi+\delta)=-180 \implies x - 245 = -180 \therefore \boxed{x = 65^o}
}[/tex3]