In two supplemantary angles, the measure of one angles is 6 more than the twice the measure of the other. the measure of these two angles are

The measurements of the 2 (TWO) supplementary angles are:

           58° and 122° .

Explanation:

Two supplementary angles:

Angle 1:  "x:

Angle 2:  "(6 + 2x)"

        All supplementary angles, by definition, add up to 180 degrees,  so given that the 2 (two) angles are supplementary:

(x) + (6 + 2x) = 180 ;  Find "x"  and "(6 + 2x)" .

   x + 6 + 2x = 180 ;

      3x + 6 = 180 ;

   Subtract "6" from each side of the equation ;

      3x + 6 − 6  = 180 − 6 ;

          3x = 174 ;

Divide each side of the equation by "3"  ;
  to isolate "x" on one side of the equation ; and to solve for "x" ;

          3x / 3 = 172 / 3 ;

               x = 58 ;

So: 

Angle 1:  "x" :  x = 58 .

Angle 2:  "(6 + 2x)" =  " 6 + 2(58) = 122 .

122 + 58 =? 180 ?  Yes!

So, the measurements of the 2 (TWO) supplementary angles are:
           58° and 122° .