Question

sabendo que os ângulos Ê e F são suplementares e que Ê= 2x+5° F=x+7°, ache o valor de Ê e F

Answer 1

Se são suplementares, a soma dos ângulos E e F será igual a 180°, logo:

$\hat{E}~+~\hat{F}~=~180^\circ\\\\\\(2x+5^\circ)~+~(x+7^\circ)~=~180^\circ\\\\\\3x~+~12^\circ~=~180^\circ\\\\\\3x~=~180^\circ~-~12^\circ\\\\\\3x~=~168^\circ\\\\\\x~=~\dfrac{168^\circ}{3}\\\\\\\boxed{x~=~56^\circ}$

Com o valor de "x", podemos determinar quanto vale cada angulo:

$\hat{E}~=~2x~+~5^\circ\\\\\\\hat{E}~=~2\cdot56^\circ~+~5^\circ\\\\\\\hat{E}~=~112^\circ~+~5^\circ\\\\\\\boxed{\hat{E}~=~117^\circ}\\\\\\\\\hat{F}~=~x~+~7^\circ\\\\\\\hat{F}~=~56^\circ~+~7^\circ\\\\\\\boxed{\hat{F}~=~63^\circ}$