SOLUTION: Determine the measure(in degrees) of an angle whose complement is four-ninths its supplement.

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Question 129552: Determine the measure(in degrees) of an angle whose complement is four-ninths its supplement.
Answer by solver91311(24713) About Me  (Show Source):
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Let x be the angle. The complement of the angle is then 90 - x. The supplement is 180 - x.

The complement of an angle (90 - x) is (=) four-ninths (4/9) of (* - meaning multiply) its supplement (180 - x):

90-x=%284%2F9%29%28180-x%29

Multiply both sides by 9 then distribute the 4:
810-9x=720-4x

Add 4x to both sides:
810-5x=720

Add -810 to both sides:
-5x=-90

Divide both sides by -5:
x=18

The measure of the angle is 18 degrees.

Check:
The complement of an angle that measures 18 degrees measures 72 degrees. The supplement of an angle that measures 18 degrees is 162 degrees. %284%2F9%29%28162%29=4%2A18=72. Answer checks.