Question 129552
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=(4/9)(180-x)}}}


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.  {{{(4/9)(162)=4*18=72}}}.  Answer checks.