Questões Perdidas ⇒ Solucionário:Racso - Cap VIII - Problemas de Geometria y Como Resolverlos - I Edição - Ex:08 Tópico resolvido

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Problema Proposto
8 - Na figura calcular "x", se AB = BC, [tex3]\measuredangle BPQ = 50^\circ e~ \measuredangle BCQ = 20^\circ[/tex3].

Resposta

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B) 110^o (Resposta errada do livro C) 140^o)

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[tex3]\measuredangle APQ \implies \overset {\LARGE{\frown}}{ADQ}=260^O \therefore \measuredangle AOQ = 100^o\\
\triangle AQD(retângulo) \measuredangle OAQ = \measuredangle OQA = 40^o\\
\measuredangle ODQ = \measuredangle OQD = 50^o\\
\triangle ABD (isosceles) \therefore \measuredangle PAQ =30^o \implies \theta = 20^o\\
\therefore \boxed{\color{red}x = 90+20 = 110^o}
[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\measuredangle APQ \implies \overset {\LARGE{\frown}}{ADQ}=260^O \therefore \measuredangle AOQ = 100^o\\
\triangle AQD(retângulo) \measuredangle OAQ = \measuredangle OQA = 40^o\\
\measuredangle ODQ = \measuredangle OQD = 50^o\\
\triangle ABD (isosceles) \therefore \measuredangle PAQ =30^o \implies \theta = 20^o\\
\therefore \boxed{\color{red}x = 90+20 = 110^o}
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