Final answer:
The value of x is 20, found by equating the expressions for the congruent angles and solving for x.
Step-by-step explanation:
To solve for the value of x using the given congruent triangles ARST and ARUT with angles S and U, we set their measures equal to each other because congruent triangles have congruent corresponding parts. Therefore, the equation is (5x - 11) degrees = (4x + 9) degrees.
By solving the equation, we subtract 4x from both sides to get x - 11 = 9, and then add 11 to both sides to obtain x = 20. Thus, the value of x is 20 degrees.