Quadriláteros - 2003 - Vol 4 ⇒ Problema 62 - Quadrilateros -Vol. 4 Tópico resolvido

[petrasMOD]

Calcular x^o.

Resposta

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Gabarito: E) 60^o

[petrasMOD]

Traçar CF, FD [tex3] \mathtt{\rightarrow \triangle ACF_{(isosc.)}\therefore ACF \cong \angle AFC = 80^o \\
AC_{(bissetriz)} \implies\angle ABE \cong \angle AME = 80^o \\
Traçar~AG_{(bissetriz)}
\therefore BC = CM = FM \implies \\
\triangle BCM_{(isosc)}: \angle = \angle ECM \cong \angle BCE = 40^o \\\angle CBE \cong \angle CME= 50^o
\\
\triangle FMC_{(isosc)} \therefore \angle FM = 100^o \implies \angle DMF = 180^o = 50^o - 100^o = 30^o \\
NECG_{(ciclico)} \angle ECG \cong \angle AME = 80^o \\
\triangle CDF: \angle DCF = 80^o -x \implies \angle FDC = 180^o - 80^o - (80^o - x) = 20^o + x\\
\therefore \angle FDC+ 30^o = 180^o - 70^o \implies 20^o + x = +30^o = 50^o \implies \boxed{x=60^o }}


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