X°,y° and z° are three angles lying on a straight line. if x°=2y° and z°=3y°,find he value of y

  " y = 30° "  .

Note:  The sum total of the measure of all angles lying on a straight
             line is 180°.

So;   x + y + z = 180 .

Given:    x =  2y ;
              z  =  3y ;

Find the value of:  " y " ;

Since:   x + y + z = 180 ; 

Substitute:  "2y"  for  "x" ; 
          and:  "3y"  for  "z" ;

       2y + y + 3y = 180 ;

                6y = 180 ;

  Divide EACH SIDE of the equation by "6" ; to isolate "y" on one side of the equation; and to solve for "y" ;

       6y/ 6 = 180 / 6 ; 

             y = 30 ;

Let us check our work;

     2y + y + 3y = 180 ;

Substitute our solved value:  "30" ; for "y" ; in the equation; to see if the equation holds true:

  2(30)  +  30  +  3(30)  =?  180 ?

   60  +  30  +  90  = ?  180 ?

             90  +  90  = ?  180 ?  Yes!