Question

Determine o valor de x nos triângulos a seguir. ​


Sem gracinhas por favor eu preciso urgentemente

Answer 1

✅ Respostas:

• $\rm a)$ No triângulo retângulo $\rm \triangle CAB$, $\rm x = 45^{\circ}$
• $\rm b)$ No triângulo equilátero $\rm \triangle OPR$, $\rm x = 60^{\circ}$
• $\rm c)$ No triângulo $\rm \triangle ABC$, $\rm x = 59^{\circ}$

 

☁️ Vamos nos sustentar no fato de que o somatório dos ângulos internos de um triângulo equivale a 180°

$\Large \underline{\boxed{\boxed{\textstyle \qquad \rm \sum_{\hat{a}_i} \triangle = 180^{\circ} \qquad }}}$

 

⚠️ Obs.: $\large \rm \square \!\!\! \cdot \;$ refere-se a ângulos de 90°.

 

✍️ Item a)

$\large\begin{array}{lr}\rm x^{\circ} + 45^{\circ} + 90^{\circ} = 180\\\\\rm x^{\circ} + 135^{\circ} = 180^{\circ}\\\\\rm x^{\circ} = 180^{\circ} - 135^{\circ} \\\\\red{\underline{\boxed{\rm \therefore\:x^{\circ} = 45^{\circ}}}}\end{array}$

 

✍️ Item b)

$\large\begin{array}{lr}\rm x^{\circ} + x^{\circ} + x^{\circ} = 180^{\circ}\\\\\rm 3x^{\circ} = 180^{\circ}\\\\\rm x^{\circ} = \dfrac{180^{\circ}}{3} \\\\\red{\underline{\boxed{\rm \therefore\: x = 60^{\circ}}}}\end{array}$

 

✍️ Item c)

$\large\begin{array}{lr}\rm x + x +1 +x +2 = 180^{\circ}\\\\\rm 3x^{\circ} + 3^{\circ} = 180^{\circ}\\\\\rm 3x^{\circ} = 180^{\circ} - 3^{\circ} \\\\\rm 3x^{\circ} = 177^{\circ} \\\\\rm x^{\circ} = \dfrac{177^{\circ}}{3} \\\\\red{\underline{\boxed{\rm \therefore\:x^{\circ} = 59^{\circ}}}}\end{array}$

 

✅ Esses são os valores de $\rm \green{x}$!

 

❏ Seção de links para complementar o estudo sobre ângulos internos de um triângulo, triângulos:

• https://brainly.com.br/tarefa/31639567

$\rule{7cm}{0.01mm}\\\texttt{Bons estudos! :D}\\\rule{7cm}{0.01mm}$