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° .