Question

Help? Show work!

m∠ABC=(6x+8)° and m∠DEF=(12x-8)°.
If ∠ABC and ∠DEF are supplementary,what
is the measure of each angle?

Answer 1

→ (6x + 8) + (12x - 8) = 180°

→ 6x + 8 + 12x - 8 = 180°

→ 18x = 180°

→ x = 180 ÷ 18

→ x = 10°

Now, we are given that m∠ABC = (6x+8) just subsitute the value of x in it .

→ m∠ABC = (6x + 8)

→ m∠ABC = (6 × 10 + 8)

→ m∠ABC = 60 + 8

→ m∠ABC = 68°

Similarly, subsitute the value of x in m∠DEF = (12x - 8)° we get :

→ m∠DEF = (12x - 8)°

→ m∠DEF = (12 × 10 - 8)

→ m∠DEF = 120 - 8

→ m∠DEF = 112°

Answer 2

m∠ABC = 68°

m∠DEF = 112°

Explanation:

Supplementary angles are angles that add up to 180 degrees (they form a straight line).

If ∠ABC and ∠DEF are supplementary, that means that they add up to 180. We can write this in an equation:

• (6x + 8) + (12x - 8) = 180

Combine like terms.

• 18x = 180

Divide both sides by 18.

• x = 10

Find the measure of each angle by substituting 10 for x into both expressions for the angles.

m∠ABC = (6x + 8)°

• 6(10) + 8 = 68°

m∠DEF = (12x - 8)°

• 12(10) - 8 = 112°