Answer:
∡QST=130°
Explanation
∡RST is going to be the sum of ∡RSQ+∡QST and that will help us find x. Since we know ∡RST=172°, we can set ∡RSQ+∡QST=172°. With this, you can substitute in the values for the 2 angles, giving us (x+50)+(x+138)=172. To solve this, we can combine the variables and the constants to give us 2x+188=172. Using our rules we can subtract 188 from each side giving us 2x=-16. Finally, we can divide by 2 from each side to get x=-8. With this, we can substitute x into the equation we were given for ∡QST. With -8 substituted in, the equation is ∡QST=(-8)+138 making the final answer ∡QST=130°.