Quadriláteros - 2003 - Vol 4 ⇒ Problema 66 - Quadrilateros -Vol. 4 Tópico resolvido

[petrasMOD]

Calcular x^o.

Resposta

---

Gabarito: C) 30^o

[petrasMOD]

Traçar AE [tex3]
\angle ADB = 50^o\\
\angle DAC = 60^o\\
Traçar~AE: \angle DAE =20^o \implies \triangle DAE_{(isosc)} \therefore AE = AD = AB \\
\angle AED \cong \angle ADE = 80^o \\
\angle EAC = 40 \implies \triangle EAC_{(isosc.)} \implies AE=EC\\
\triangle AEB_{(isosc)}~mas \angle EAB = 60^o \therefore \triangle AEB_{(equil)} \implies AE = AB = BE\\
\angle BEC = 180^o - (60^o +80^o ) = 40^o \\
\triangle AEC_{(isosc)} \implies EC = AE = BE \therefore \triangle BEC_{(isosc)}\\
x+40^o = 70 \implies \boxed{x = 30^o } [/tex3]