SOLUTION: The sum of the supplement and complement of an angle is 130 degrees. Find measure of the angle.

Question 433423: The sum of the supplement and complement of an angle is 130 degrees. Find measure of the angle.
Found 2 solutions by stanbon, dudeantariksh:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The sum of the supplement and complement of an angle is 130 degrees. Find measure of the angle.
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Let the angle be "x".
supplement: 180-x
complement: 90-x
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Equation:
180-x+90-x = 130
270-2x = 130
2x = 140
x = 70 degrees
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Cheers,
Stan H.
Answer by dudeantariksh(10) (Show Source): You can put this solution on YOUR website!
hi there!!
well, we are given the sum of the COMPLEMENT and SUPPLEMENT of the given angle..
first let us recollect 2 important concepts.
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COMPLEMENTARY angles.
the angles whose measures sum up to 90 DEGREES, then they are called COMPLEMENTARY ANGLES.
Then, each of the angles is called the complement of the other.
thus, if , angleA+ angleB = 90, THEN angleA is the complement of angleB ,
and angleB is the complement of angleA.
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SUPPLEMENTARY angles
the angles whose measures sum up to 180 DEGREES, then they are called SUPPLEMENTARY angles.
hen, each of the angles is called the SUPPLEMENT of the other.
thus, if , angleA+ angleB = 180, THEN angleA is the suppement of angleB ,
and angleB is the supplement of angleA.
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now. in the given question, let's assume the value of the given angle to be X degrees.
now we know that the sum of the complement of an angle and the angle itself is 90degrees.
thus, the complement of the angle = 90-X
similarly,
the supplement of the given angle = 180-X.
now as per the given conditon,
complement of given angle + supplement of given angle = 130
thus,
90-X + 180-X = 130
THUS,
90+180-X-X = 130
THUS,
270 - 2X = 130
THEREFORE, WE SUBTRACT 270 FROM BOTH THE SIDES & WE GET,
- 2X = 130 - 270
THEREFORE,
-2X = -140
THEREFORE,
2X = 140
THEREFORE,DIVIDING BOTH SIDES BY 2, WE GET,
X = 70
THUS, THE GIVEN ANGLE IS 70 DEGREES IN MEASURE.

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