SOLUTION: ∠DEF and ∠ABC are supplementary angles and ∠DEF is four times as large as ∠ABC. Determine the measure of each angle. If someone could help me with this,

Algebra ->  Angles -> SOLUTION: ∠DEF and ∠ABC are supplementary angles and ∠DEF is four times as large as ∠ABC. Determine the measure of each angle. If someone could help me with this,      Log On


   

Question 480050: ∠DEF and ∠ABC are supplementary angles and ∠DEF is four times as large as ∠ABC. Determine the measure of each angle.
If someone could help me with this, I would be grateful. Also, to get a better understanding of this, would you mind showing me how you arrived to your answers? Thank you so much!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
∠DEF and ∠ABC are supplementary angles and ∠DEF is four times as large as ∠ABC.
supplementary angles: they add up to 180°

∠DEF=4*∠ABC.......substitute ∠DEF in ∠DEF + ∠ABC=180°

∠DEF + ∠ABC=180°

4*∠ABC + ∠ABC=180°

5*∠ABC =180°

∠ABC =180%2F5°

∠ABC =36°....now find ∠DEF

∠DEF=4*∠ABC

∠DEF=4*36°

∠DEF=144°