We need to use the exterior angle theorem...
the nonadjacent angles of 107 degrees will equal to 107 degrees.
9 + 4x + 11x + 8 = 107
17 + 15x = 107
15x = 90
x = 6
Check...
measure of angle KUT = 9 + 4x = 9 + 4(6) = 33 degrees
measure of angle STU = 11x + 8 = 11(6) + 8 = 66 + 8 = 74 degrees
measure of angle UST = 180 - 107 = 73 degrees
33 + 74 + 73 = 180 degrees (sum of interior angles of triangle equals to 180)
