SOLUTION: Measure of the complement of an angle is one-fourth the measure of the supplement of the angle. Find the measure of the angle.

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Question 209978: Measure of the complement of an angle is one-fourth the measure of the supplement of the angle. Find the measure of the angle.
Answer by Earlsdon(6098) About Me  (Show Source):
You can put this solution on YOUR website!
Let the angle be A so its complement is (90-A) and its supplement is (180-A).
The problem can be expressed as:
%2890-A%29+=+%281%2F4%29%28180-A%29 Simplify and solve for A. Multiply both sides by 4.
4%2890-A%29+=+%28180-A%29 Simplify the left side.
360-4A+=+180-A Add 4A to both sides.
360+=+180%2B3A Subtract 180 from both sides.
180+=+3A Finally, divide both sides by 3.
60+=+A
The measure of the angle is 60 degrees.