9514 1404 393
Answer:
m∠T = 45°
Explanation:
The sum of angles in a triangle is 180°, so ...
(2x +10)° +(3x -9)° +(6x -19)° = 180°
11x -18 = 180 . . . . . collect terms, divide by °
11x = 198 . . . . . . . . add 18
x = 18 . . . . . . . . . . . divide by 11
Then the angle of interest is ...
m∠T = (3x -9)° = (3·18 -9)°
m∠T = 45°
_____
The other angles are ...
m∠S = 46°
m∠U = 89°