Triângulos - 2008 - Vol. 2 ⇒ 011 - Triângulos - 2008 Tópico resolvido

[petrasMOD]

Segundo o gráfico mostrado, calcular (x+ y ).

Resposta

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Gabarito: 320^o

[petrasMOD]

[tex3]\mathsf{
\triangle BED: 2\theta = 180-x+180-3\alpha \implies x = 360-3\alpha - 2\theta(I)\\
\triangle BEC:180-y+180-2\alpha+180-3\theta=180 \implies y = 360-2\alpha - 3\theta(II)\\
(I)+(II) = x+y = 720-5(\alpha+\theta)\\
\triangle ABE:2\alpha+2\theta+20 = 180 \implies \alpha+\theta = 80^o \\
Substituindo: x+y = 720-5(80) = \boxed{320^o }
}[/tex3]