m∠ABC=(6x+8)° and m∠DEF=(12x-8)°. If ∠ABC and ∠DEF are supplementary, what is the measure of each angle? I CAN'T ANSWER THIS QUESTION FOR THE LIFE OF ME!
you forgot what it means for two angles to be supplementary: their sum is 180°
So, to find x, set
(6x+8) + (12x-8) = 180
Now that you know that x=10, you can find the angles.
If ∠ABC and ∠DEF are supplementary angles, it means that the sum of their measures is 180°.
We are given that m∠ABC = (6x+8)° and m∠DEF = (12x-8)°.
So, we can write the equation:
(6x+8)° + (12x-8)° = 180°
Simplifying the equation:
6x + 8 + 12x - 8 = 180
18x = 180
x = 180/18
x = 10
Now we can substitute the value of x back into the expressions for the angles:
m∠ABC = (6x+8)° = (6(10)+8)° = 68°
m∠DEF = (12x-8)° = (12(10)-8)° = 112°
Therefore, the measure of ∠ABC is 68° and the measure of ∠DEF is 112°.
To find the measure of each angle, we can set up an equation since the angles are supplementary.
Supplementary angles add up to 180 degrees. So, we can write the equation:
m∠ABC + m∠DEF = 180°
Substitute the given expressions for the angles:
(6x + 8) + (12x - 8) = 180
Combine like terms:
18x = 180
Divide both sides by 18:
x = 10
Now that we have the value of x, we can substitute it back into the expressions for the angles:
m∠ABC = 6x + 8
m∠ABC = 6(10) + 8
m∠ABC = 68°
m∠DEF = 12x - 8
m∠DEF = 12(10) - 8
m∠DEF = 112°
Therefore, the measure of angle ABC is 68 degrees and the measure of angle DEF is 112 degrees.