Question

38.A figura abaixo representa o quadrilátero FOCA. Sabe-se que CT é a bissetriz do
ângulo OČA, AF // OC, FÃO=70°CÍA= 100°. Qual é a medida do ângulo x?

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{F\widehat AO = 70\textdegree}$

$\mathsf{A\widehat FO = 60\textdegree}$

$\mathsf{F \widehat OA = 180\textdegree - F\widehat AO - A\widehat FO}$

$\mathsf{F \widehat OA = 180\textdegree - 70\textdegree - 60\textdegree}$

$\mathsf{F \widehat OA = 50\textdegree}$

$\mathsf{C \widehat OT = 180\textdegree - F \widehat OA - 60\textdegree}$

$\mathsf{C \widehat OT = 180\textdegree - 50\textdegree - 60\textdegree}$

$\mathsf{C \widehat OT = 70\textdegree}$

$\mathsf{C \widehat TO = 180\textdegree - C \widehat TA}$

$\mathsf{C \widehat TO = 180\textdegree - 100\textdegree}$

$\mathsf{C \widehat TO = 80\textdegree}$

$\mathsf{O \widehat CT = 180\textdegree - C \widehat TO - C \widehat OT}$

$\mathsf{O \widehat CT = 180\textdegree - 80\textdegree - 70\textdegree}$

$\mathsf{O \widehat CT = 30\textdegree}$

$\mathsf{x = 180\textdegree - C \widehat TA - A \widehat CT}$

$\mathsf{x = 180\textdegree - 100\textdegree - 30\textdegree}$

$\boxed{\boxed{\mathsf{x = 50\textdegree}}}$