SOLUTION: 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 w
Algebra.Com
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.
.
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.
RELATED QUESTIONS
The sum of three times an angle and twice its complement is 215. Find the measures of the (answered by Seutip)
The sum of three times an angle and twice its complement is 215. Find the measures of the (answered by math-vortex)
the sum of three times an angle and twice its complement is 215. what are the measures of (answered by algebrahouse.com)
Find the measure of an angle such that the sum of its supplement and four times its... (answered by Boreal)
The measure of a complement of an angle is ten less than three times the measure of the... (answered by josey1)
Find the angle which is four times its... (answered by LinnW)
The Supplement of an angle measures 15 degrees more than four times its complement. Find... (answered by gonzo)
The supplement of an angle measures three times its complement. What is the original... (answered by josmiceli)
The sum of three times an angle and its complement is 114.find the measure of the... (answered by Cromlix)