M∠abc=(6x+8)° and m∠def=(12x−8)°. if ∠abc and ∠def are supplementary, what is the measure of each angle?

Given: m∠ABC=(6x+8)° and m∠DEF=(12x−8)°.

To find: measure of angles m∠ABC and m∠DEF.

Soltution: It is said ∠ABC and ∠DEF are supplementary.

Sum of supplementary angles is 180°.

So, we can add the given values of angles ∠ABC and ∠DEF and set it equal to 180°.

m∠ABC +  m∠DEF= 180°

Plugging values of ∠ABC and ∠DEF in above equation.

(6x+8)  + (12x−8) = 180.

Removing parenthese,

6x+8 +12x - 8 = 180.

Combining like terms

6x+12x = 18x and 8-8 = 0.

Therefore, 6x+8 +12x - 8 = 180 would become 18x  = 180.

Dividing both sides by 18, we get

18x/18 = 180/18

x=10.

Plugging value of x in given expessions for m∠ABC and m∠DEF.

m∠ABC=6x+8 = 6* 10 +8 = 60 +8 = 68.

m∠DEF=12x−8 = 12*10 -8 = 120 - 8 = 112.

Therefore, m∠ABC= 68° and m∠DEF =112° .