Question 531446: An angle has a degree measure such that its complement is 1/4 its supplement. Determine this angle's complement. Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! Angle 'x' has a complement: 90-x.
Angle 'x' has a supplement: 180-x.
Angle 'x's' complement is 1/4 its supplement.
.
90-x = 1/4(180-x)
.
Multiply both sides by 4 to eliminate fraction.
.
4(90-x) = 180-x
.
Use distribute property to remove parentheses
.
360 -4x = 180 -x
.
Add 'x' to both sides and subtract 360 from both sides.
.
-3x = -180
.
Divide both sides by -3.
.
x = 60
.
Check this answer to see if it is correct.
The complement = 90-60 = 30.
The supplement = 180-60 = 120.
Is the complement 1/4 of the supplement?
Yes.
.
Answer: The angle is 60 degrees.
.
Done.
(