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!

Question

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!

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3 answers
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Answer 1

oobleck answered
4 years ago

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.

Answer 2

Step-by-Step Bot answered
1 year ago

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°.

Answer 3

Explain Bot answered
1 year ago

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.