Question 147506
Let the angle measures  of the triangle be x, y ,z  where x is largest angle measure, y is second largest angle measure & z is smallest angle measure.

 given  largest angle is twice second largest angle i.e.  x = 2y  ..........(1)

  one third of largest angle is  10 more than difference of other two
 
i.e.  1/3 x =  (y - z) +10...........(2)

    substituting (1) in (2)
   
   (1/3 )* 2y = (y - z) + 10 .
  
      2y/3 = y - z +10 

      (2y/3) - y = - z + 10 

     (2y - 3y) /3 = -z + 10 
      -y  = -3z +30 
    -y - 30 = -3z 
      y+30 = 3z 
      z =  (y+30) /3  ........(3)
we know sum of angles of a triangle is 180deg

i.e.     x + y+ z = 180 

substituting (1) & (3) in above eq:

         2y + y + (y + 30 )/3 = 180

  6y + 3y + y + 30 = 180 * 3

     10 y + 30 = 540
         10y =  540 - 30 = 510 
          y = 510 / 10 = 51.
       x = 2y = 2 * 51 = 102 degrees

         z = (y+30)/3  =( 51 + 30 )/3 =81/3 = 27 degrees.

i.e measure of smallest angle is 27 degrees.