Question

Valores de x dos ângulos complementares x+10 e 2×+20

Answer 1

A soma de dois ângulos complementares é igual a $90^{\circ}$.

Pelo enunciado, os ângulos $x+10^{\circ}$ e $2x+20^{\circ}$ são complementares.

Logo:

$x+10^{\circ}+2x+20^{\circ}=90^{\circ} \iff 3x+30^{\circ}=90^{\circ} \iff 3x=90^{\circ}-30^{\circ}$

$3x=60^{\circ} \iff x=\dfrac{60^{\circ}}{3} \iff \boxed{x=20^{\circ}}$

$x+10^{\circ}=20^{\circ}+10^{\circ} \iff \boxed{x+10^{\circ}=30^{\circ}}$

$2x+20^{\circ}=2\cdot20^{\circ}+20^{\circ}=40^{\circ}+20^{\circ} \iff \boxed{2x+20^{\circ}=60^{\circ}}$