Question

Determine a medida de x indicada na figura seguinte:


a) 54°
b) 76°
C)84°
D)108°

Answer 1

C) espero te ajudado

Answer 2

Explicação passo-a-passo:

Calculando o arco $AB$, sabendo que $A\^DB=36^{\circ}$:

$\dfrac{AB}{2}=A\^DB\\\\\dfrac{AB}{2} =36^{\circ} \\\\AB=2.36^{\circ} \\\\\boxed{AB=72^{\circ} }$

Calculando o arco $CD$, sabendo que $C\^BD=40^{\circ}$:

$\dfrac{CD}{2}=C\^BD\\\\\dfrac{CD}{2} =40^{\circ} \\\\CD=2.40^{\circ} \\\\\boxed{CD=80^{\circ} }$

Calculando o ângulo x:

$x=\dfrac{AB+CD}{2}\\\\x=\dfrac{72^{\circ}+80^{\circ} }{2} \\\\x=\dfrac{152^{\circ}}{2}\\\\\boxed{\boxed{x=76^{\circ}}}$

Resposta B