Question 175388: An angle measures 15 degrees more than twice its supplement. Find the measure of the supplement. Found 2 solutions by Mathtut, gonzo:Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website! let the two angles be a and b.
:
a=2b+15.....eq 1
:
a+b=180.....eq 2
:
take a's value from eq 1 and plug it into eq 2
:
2b+15+b=180
:
3b=165
: degrees
: degrees
You can put this solution on YOUR website! let x = the angle
180 - x = the supplement of the angle.
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the angle measures 15 degrees more than twice its supplement.
x = 15 + (2 * (180-x))
simplify to get:
x = 15 + 360 - 2x
add x to both sides to get:
3x = 375
divide both sides by 3 to get:
x = 125 degrees
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if x = 15 + 360 - 2x, then
x = 15 + 360 - 250 = 375 - 250 = 125 degrees.
this confirms the original equation so the answer is good.
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the measure of the angle is 125 degrees.
this, however, is not what they asked.
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the measure of the supplement is 180 - 125 degrees = 55 degrees
the answer is:
the measure of the supplement is 55 degrees.
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to confirm again:
x = 15 + 2*55 = 15 + 110 = 125 degrees.
answer is confirmed.
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