Question

1.1.f pairs of angles, part 2, homework
started: sep 4 at 7:33pm
question 1 of 6
$m\angle abc=(6x + 8)^{circ}$ and $m\angle def=(12x - 8)^{circ}$. if $\angle abc$ and $\angle def$ are supplementary, what is the measure of each angle?
$m\angle abc = 68^{circ};m\angle def = 122^{circ}$
$m\angle abc = 68^{circ};m\angle def = 112^{circ}$
$m\angle abc = 47^{circ};m\angle def = 112^{circ}$
$m\angle abc = 47^{circ};m\angle def = 122^{circ}$

Explanation:

Step1: Sum of supplementary angles

$(6x + 8) + (12x - 8) = 180$

Step2: Simplify equation

$18x = 180$

Step3: Solve for x

$x = 10$

Step4: Calculate m∠ABC

$6(10) + 8 = 68^\circ$

Step5: Calculate m∠DEF

$12(10) - 8 = 112^\circ$

Answer:

B. m∠ABC = 68°; m∠DEF = 112°