Final answer:
To make lines a and b parallel, set the corresponding angle (9x + 11) degrees equal to 74 degrees and solve for x. Simplify the equation to find that x = 7.
Step-by-step explanation:
To find x so that line a is parallel to line b, we use the concept of corresponding angles. Since line a has an angle of 74 degrees, line b, being parallel, must have a corresponding angle that is equal to this. The angle for b is given as (9x + 11) degrees. We set this equal to 74 degrees and solve for x:
9x + 11 = 74
Now we subtract 11 from both sides to isolate the term with x:
9x = 74 - 11
9x = 63
Finally, we divide by 9 to find x:
x = 63 / 9
x = 7
The converse used in this situation is that if the corresponding angles are equal, then the lines are parallel.