Final answer:
The value of x for which line 'a' is parallel to line 'b' is 51°.
Step-by-step explanation:
In order for line 'a' to be parallel to line 'b', the corresponding angles formed by the two lines must be equal. In this case, we have:
∠1 = 90°
∠2 = 20°
∠3 = 10°
∠4 = 9°
We need to find the value of x that would make line 'a' parallel to line 'b'.
Since ∠1 is a right angle (∠1 = 90°) and ∠2 + ∠3 + ∠4 = 20° + 10° + 9° = 39°, the remaining angle, x, can be found by subtracting the sum of the given angles from 90°:
x = 90° - (20° + 10° + 9°) = 90° - 39° = 51°
Therefore, the value of x for which line 'a' is parallel to line 'b' is 51°.