SOLUTION: Two angles are supplementary. If the larger angle measures 60 less than twice the smaller, find the measure of the larger angle.

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Question 882292: Two angles are supplementary. If the larger angle measures 60 less than twice the smaller, find the measure of the larger angle.
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let L = the larger angle in degrees
Let S = the smaller angle in degrees
Then we have
(1) L + S = 180 because they are supplements and add to 180 degrees.
And the problem statement gives us
(2) L = 2*S - 60
Now substitute L of (2) into (1) and get
(3) 2*S - 60 + S = 180 or
(4) 3*S = 180 + 60 or
(5) 3*S = 240 or
(6) S = 240/3 or
(7) S = 80
Use S of (7) in (1) to get
(8) L + 80 = 180 or
(9) L = 100
Let's check these values in (2).
Is (100 = 2*80 - 60)?
Is (100 = 160 - 60)?
Is (100 = 100)? Yes
Answer: The larger angle of the supplementary angles is 100 degrees, the smaller is 80 degrees.