Question

Com os dados da figura, pode-se concluir que o valor de X é: a) 60° b) 100° c) 120° d) 130° e) 140°

Answer 1

Explicação passo-a-passo:

• Triângulo ADG

$\sf 180^{\circ}-\beta+180^{\circ}-\beta+180^{\circ}-x=180^{\circ}$

$\sf x+2\beta=360^{\circ}$

$\sf 2\beta=360^{\circ}-x$

$\sf \beta=180^{\circ}-\dfrac{x}{2}$

• Triângulo DEF

$\sf 180^{\circ}-x+180^{\circ}-5\alpha+90^{\circ}=180^{\circ}$

$\sf x+5\alpha=270^{\circ}$

$\sf 5\alpha=270^{\circ}-x$

$\sf \alpha=54^{\circ}-\dfrac{x}{5}$

• Quadrilátero CEDG

$\sf x+\alpha+\beta+90^{\circ}=360^{\circ}$

$\sf x+\alpha+\beta=270^{\circ}$

$\sf x+54^{\circ}-\dfrac{x}{5}+180^{\circ}-\dfrac{x}{2}=270^{\circ}$

$\sf x-\dfrac{x}{5}-\dfrac{x}{2}=36^{\circ}$

$\sf 10x-2x-5x=360^{\circ}$

$\sf 3x=360^{\circ}$

$\sf x=\dfrac{360^{\circ}}{3}$

$\sf x=120^{\circ}$

Letra C