Question 162874
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
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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
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Since they asked for the "smallest" angle, it would then be 85 degrees.