Given that x = 9, the angle (6x+9)° is also 63°. This means that the angles are equal, and therefore the lines are parallel when x = 9.
How do we find if the lines are parallels?
The property of corresponding angles, tell that if two lines are cut by a transversal and the corresponding angles are equal, the lines are parallel.
The corresponding angle to the 63-degree angle is (6x+9)°. If the lines are parallel, this angle should also be 63° when x=9.
(6x+9)° ⇒ (6(9) + 9)°
(54 + 9) = 63°
When x=9, the calculated angle (6x+9) is indeed 63 degrees. Since the angles are equal, this means that the lines are parallel when x = 9.