Final answer:
The value of x is 4.5.
Step-by-step explanation:
To find the value of x, we need to set the measures of angles 1 and 5 equal to each other: 11x-9 = 7x+9.
Next, we solve for x:
11x-7x = 9+9
4x = 18
x = \frac{18}{4}
x = 4.5
Therefore, the value of x is 4.5.