SOLUTION: <ABC and <PQR are supplementary angles and <ABC is eleven times as large as <PQR. Determine the measure of each angle.

Algebra ->  Angles -> SOLUTION: <ABC and <PQR are supplementary angles and <ABC is eleven times as large as <PQR. Determine the measure of each angle.      Log On


   

Question 199652:
Answer by tutorvolunteer(9) About Me  (Show Source):
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Let's use variables in solving: Since x and y are supplementary, x+y = 180 by the definition of supplementary angles.
Also, x is 11 times as large as y, so x = 11y.
Now we have 2 equations with 2 variables and can solve using a variety of methods for systems of equations (i.e. substitution, multiplication with addition, etc)
Plug in x=11y to x+y=180, so 12y = 180, and y = 15. Using this, we find that x = 165.