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Question 113269: Two angles are supplementary, and one is 5° more than six times the other. Find the larger angle.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let the two angles be x and y.
If two angles are supplementary, then their sum is 180 degrees, so you can write:
1) x + y = 180 Rewrite this as:
2) x = 180-y
From the problem, you can write:
3) x = 6y+5 "One angle is 5 degrees more than 6 times the other"
Substitute the x from equation 2 into equation 3 and solve for y.
(180-y) = 6y+5 Add y to both sides.
180 = 7y+5 Subtract 5 from both sides.
175 = 7y Divide both sides by 7
25 = y and...
x = 180-y
x = 180-25
x = 155
The larger angle is 155 degrees.
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