Question 162874: Find the smallest angle in which the sum of the measures of the angle, three times its complement, and four times its supplement is at most 480 degrees.
I have been struggling with this problem for a while. please help
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Remember, if two angles are "supplementary" then the sum of the two angles is 180. And, if two angles are "complementary" then the sum of the two angles is 90.
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Let x = "the angle"
then
180-x = the supplement
90-x = the complement
.
From: "sum of the measures of the angle, three times its complement, and four times its supplement is at most 480 degrees." we get
x + 4(180-x) + 3(90-x) <= 480
x + 720 - 4x + 270 - 3x <= 480
990 - 6x <= 480
-6x <= -510
x >= 85 degrees
.
Since they asked for the "smallest" angle, it would then be 85 degrees.
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