Question

Determine x e y , sabendo-se que as retas a e b são paralelas​

Answer 1

Explicação passo-a-passo:

Os ângulos 10y-20° e 3y+5° são colaterais internos logo são suplementares (soma igual a 180°).

$10y-20+3y+5^{\circ} =180^{\circ} \\\\13y -15^{\circ} =180^{\circ} \\\\13y =180^{\circ} +15^{\circ} \\\\13y=195^{\circ} \\\\y=\dfrac{195^{\circ} }{13} \\\\\boxed{y=15^{\circ} }$

Os ângulos 2x+10° e 3y+5° são alternos externos logo são congruentes.

$2x+10^{\circ} =3y+5^{\circ} \\\\2x+10^{\circ} =3.15^{\circ} +5^{\circ} \\\\2x+10^{\circ} =45^{\circ} +5^{\circ} \\\\2x+10^{\circ} =50^{\circ} \\\\2x=50^{\circ} -10^{\circ} \\\\2x=40^{\circ} \\\\x=\dfrac{40^{\circ} }{2}\\\\\boxed{x=20^{\circ} }$

Os ângulos 2x+10° e z são opostos pelo vértice logo são congruentes.

$z=2x+10^{\circ} \\\\z=2.20^{\circ} +10^{\circ} \\\\z=40^{\circ} +10^{\circ} \\\\\boxed{z=50^{\circ} }$