Question

(02) calcule o valor dos ângulos (a) e(b):
Por favor alguém responder!!!!!!!!!

Answer 1

Resposta:

a=125° e b=55°

Explicação passo-a-passo:

Sendo r//s

b=55°

55°+a=180°

a=180°-55°

a=125°

Answer 2

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⠀⠀☞ O ângulo a vale 125º e o ângulo b vale 55º. ✅

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⠀⠀ Pela imagem identificamos que o ângulo b é correspondente ao ângulo de 55º, ou seja, b = 55º. ✅

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⠀⠀  Pela imagem identificamos também que o ângulo a é suplementar do ângulo de 55º, ou seja, juntos eles somam 180º.

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$\LARGE\blue{\sf a + 55 = 180}$

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$\LARGE\blue{\sf a = 180 - 55}$

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$\LARGE\blue{\sf a = 125^{\circ}}$  ✅

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______________________________

$\large\red{\sf CONGRU\hat{E}NCIA~DE~\hat{A}NGULOS}$

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⠀⠀Sejam r e s duas retas paralelas e t uma reta transversal que intercepta ambas. Temos então a formação de duas quadras de ângulos, conforme vemos na figura à seguir:

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$\setlength{\unitlength}{0.95cm}\begin{picture}(6,5)\thicklines\put(-2,2){\line(1,0){9}}\put(3,5){\line(1,0){7}}\put(0,0){\line(4,3){9}}\put(2.7,2){\circle{2}}\put(6.65,5){\circle{2}}\put(2.4,2.2){\Large\sf \hat{a}~~~~~~~\hat{b}}\put(1.5,1.5){\Large\sf \hat{d}~~~~~~\hat{c}}\put(6.3,5.3){\Large\sf \hat{e}~~~~~~~~\hat{f}}\put(5.4,4.5){\Large\sf \hat{h}~~~~~~\hat{g}}\put(-2,2.2){\LARGE\sf \overline{r}}\put(3,5.2){\LARGE\sf \overline{s}}\put(-0.3,0){\LARGE\sf \overline{t}}\end{picture}$

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$\sf (Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly$ ☹ )

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⠀⠀Pela simetria dos ângulos acima podemos definir as seguintes relações entre ângulos (≡ significa "congruente à", que é o equivalente ao = só que na geometria):

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\rm \underline{~~OPOSTOS~~}}&\\&\orange{\rm \underline{~~PELO~ V\acute{E}RTICE~~}}&\\&&\\&&\\&\orange{\sf (\hat{a} \equiv \hat{c}),~(\hat{b} \equiv \hat{d}),}&\\&&\\&\orange{\sf (\hat{e} \equiv \hat{g})~e~(\hat{f} \equiv \hat{h})}&\\&&\\\end{array}}}}}$

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\rm \underline{~~CORRESPONDENTES~~}}&\\&&\\&&\\&\orange{\sf (\hat{e} \equiv \hat{e}),~(\hat{b} \equiv \hat{f}),}&\\&&\\&\orange{\sf (\hat{h} \equiv \hat{d})~e~(\hat{c} \equiv \hat{g})}&\\&&\end{array}}}}}$

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\rm \underline{~~ALTERNOS~INTERNOS~~}}&\\&&\\&&\\&\orange{\sf (\hat{c} \equiv \hat{e})~e~(\hat{d} \equiv \hat{f})}&\\&&\end{array}}}}}$

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\rm\underline{ ~~ALTERNOS~EXTERNOS~~}}&\\&&\\&&\\&\orange{\sf (\hat{a} \equiv \hat{g})~e~(\hat{b} \equiv \hat{h})}&\\&&\end{array}}}}}$

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\rm\underline{~~SUPLEMENTARES~~}}&\\&&\\&&\\&\orange{\sf (\hat{a}~\&~\hat{b}),~(\hat{b}~\&~\hat{c}),~(\hat{c}~\&~\hat{d}),~(\hat{d}~\&~\hat{a}),}&\\&&\\&\orange{\sf (\hat{e}~\&~\hat{f}),~(\hat{f}~\&~\hat{g}),~(\hat{g}~\&~\hat{h})~e~(\hat{h}~\&~\hat{e})}&\\&&\end{array}}}}}$

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⠀⠀Lembrando que ângulos suplementares são aqueles que quando somados resultam em 180º .

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\rm\underline{~~COLATERAIS~~}}&\\&\orange{\rm(\&~SUPLEMENTARES~INTERNOS)}&\\&&\\&&\\&\orange{\sf (\hat{d}~\&~\hat{e})~e~(\hat{c}~\&~\hat{f})}&\\&&\end{array}}}}}$

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\rm\underline{~~COLATERAIS~~}}&\\&\orange{\rm(\&~SUPLEMENTARES~EXTERNOS)}&\\&&\\&&\\&\orange{\sf (\hat{a}~\&~\hat{h})~e~(\hat{b}~\&~\hat{g})}&\\&&\end{array}}}}}$

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\rm\underline{~~REPLEMENTARES~~}}&\\&&\\&&\\&\orange{\sf (\hat{a}, \hat{b}, \hat{c}~\&~\hat{d})~e~(\hat{e}, \hat{f}, \hat{g}~\&~\hat{h})}&\\&&\end{array}}}}}$

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⠀⠀Lembrando que ângulos replementares são aqueles que quando somados resultam em 360º .

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

⠀⠀Exercício semelhante:

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⠀⠀✈https://brainly.com.br/tarefa/35959398

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