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

Question 129552: Determine the measure(in degrees) of an angle whose complement is four-ninths its supplement.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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):

Multiply both sides by 9 then distribute the 4:

Add 4x to both sides:

Add -810 to both sides:

Divide both sides by -5:

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. . Answer checks.
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