Triângulos - 2008 - Vol. 2 ⇒ 061 - Triângulos - 2008 Tópico resolvido

[petrasMOD]

Calcular x + y

Resposta

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Gabarito:220^o

[petrasMOD]

[tex3]\mathsf{\triangle ABC: 180-2\alpha+2\theta+40 = 180^o \implies \alpha - \theta = 20^o(I)\\
\triangle AED: 180-2\phi+2\beta +40 = 180^o \implies \phi -\beta = 20^o (II)\\
BEGD: 360-(y+\beta+\theta)+\alpha+\phi+180-x = 360 \implies x+y = \alpha -\theta+\phi-\beta +180\\
De(I)e(II): x+y =20+20+180 = \boxed{220^o}
}[/tex3]