SOLUTION: Please help me solve this: If four times the supplement of an angle is added to eight times the angle's complement, the sum is equivalent to three straight angles. Find the measur

Algebra ->  Angles -> SOLUTION: Please help me solve this: If four times the supplement of an angle is added to eight times the angle's complement, the sum is equivalent to three straight angles. Find the measur      Log On


   

Question 780005: Please help me solve this:
If four times the supplement of an angle is added to eight times the angle's complement, the sum is equivalent to three straight angles. Find the measure of the angle that is supplementary to the complement.
Found 3 solutions by MathLover1, stanbon, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Well a straight angle is 180 degrees, so three straight angles would be three times that.
you’re looking for angle alpha
A complement is 90-alpha-the angle you’re looking for
and a supplement is 180-alpha- the angle
Set up an equation using
4%28180-alpha%29+%2B+8%2890-alpha%29+=+3%28180%29
720-4alpha+%2B720-8alpha+=+540
1440-12alpha+=+540
1440-540+=+12alpha
900+=+12alpha
900+%2F12=alpha
75=alpha

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If four times the supplement of an angle is added to eight times the angle's complement, the sum is equivalent to three straight angles. Find the measure of the angle that is supplementary to the complement.
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angle:: x
complement:: 90-x
supplement::1 180-x
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Equation:
4(180-x) + 8(90-x) = 3*180
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720-4x + 720-8x = 620
1440-12x = 620
12x = 820
x = 68 1/3 degrees
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The complement is 21 2/3 degrees
----
The supplement of this complemet is 158 1/3 degrees
===========================
Cheers,
Stan H.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me solve this:
If four times the supplement of an angle is added to eight times the angle's complement, the sum is equivalent to three straight angles. Find the measure of the angle that is supplementary to the complement.

Let angle's measurement be A

Then: 4(180 - A) + 8(90 - A) = 3(180)

720 - 4A + 720 - 8A = 540

- 4A - 8A + 1,440 = 540

- 12A = 540 - 1,440

-12A = - 900

A, or angle's measurement = %28-+900%29%2F-+12, or 75%5Eo

This 75%5Eo angle's complement is 15%5Eo, and the supplement to THIS complement is highlight_green%28165%5Eo%29

You can do the check!!

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