Question

Qual é o teorema dos ângulos externos?

Answer 1

Caso esteja pelo app, e tenha problemas para visualizar esta resposta, experimente abrir pelo navegador https://brainly.com.br/tarefa/39033074

                                                               

Teorema do ângulo externo

$\boxed{\begin{array}{l}\sf O~\hat angulo~externo~a~um~tri\hat angulo\\\sf \acute e~igual~a~soma~dos~\hat angulos~n\tilde ao-adjacentes.\\\underline{\rm demonstrac_{\!\!,}\tilde ao\!:} \\\sf perceba~que~os~\hat angulos~\mu~e~\theta~s\tilde ao~suplementares.\\\sf portanto~\\\sf \mu+\theta=180^\circ\\\sf a~soma~dos~\hat angulos~internos~de~um~tri\hat angulo~vale~180^\circ.\\\sf portanto\\\sf \mu+\alpha+\beta=180^\circ\\\sf como~180^\circ=180^\circ~podemos~escrever:\\\sf \mu+\theta=\mu+\alpha+\beta\end{array}}$

$\boxed{\begin{array}{l}\underline{\rm subtraindo~\mu~dos~dois~lados~temos:}\\\sf\mu+\theta-\mu=\mu+\beta+\alpha-\mu\\\underline{\sf DA\acute I:}\\\sf \theta=\alpha+\beta~~~\bf c\cdot q\cdot d\end{array}}$

$\underline{\rm exemplo~de~aplicac_{\!\!,}\tilde ao.}\\\sf ca\ell cule~o~valor~de~x~na~figura.\\\underline{\bf soluc_{\!\!,}\tilde ao:}\\\rm observe~a~figura~que~anexei.\\\large\boxed{\begin{array}{l}\sf pelo~teorema~do~\hat angulo~externo~temos:\\\sf 5x=3x+110^\circ\\\sf 5x-3x=110^\circ\\\sf 2x=110^\circ\\\sf x=\dfrac{110^\circ}{2}\\\sf x=55^\circ\end{array}}\blue{\checkmark}$