Calculate the values of the marked angles in each diagram involving parallel lines.

Here are the step-by-step solutions for each problem on the worksheet. I have checked the calculations for parallel lines, alternate interior angles, corresponding angles, and supplementary angles.

1.
The two marked angles are alternate interior angles. When lines are parallel, alternate interior angles are equal.
* $x = 72$

2.
First, find the angle vertically opposite to the $48^\circ$ angle; it is also $48^\circ$. The angle $x$ and this $48^\circ$ angle are consecutive interior angles (same-side interior), which means they add up to $180^\circ$.
* Calculation: $180 - 48 = 132$
* $x = 132$

3.
The angle marked $60^\circ$ and angle $x$ are alternate interior angles. They are equal.
* $x = 60$

4.
The angle marked $55^\circ$ and angle $x$ are corresponding angles. Corresponding angles are in the same position at each intersection and are equal.
* $x = 55$

5.
Angle $x$ and the angle marked $96^\circ$ are vertical angles (opposite each other where lines cross). Vertical angles are always equal.
* $x = 96$

6.
The angle marked $105^\circ$ and angle $x$ are alternate exterior angles. Alternate exterior angles are equal.
* $x = 105$

7.
The angle marked $131^\circ$ and angle $x$ are corresponding angles. They are in the same relative position at each intersection.
* $x = 131$

8.
Angle $x$ and the angle marked $112^\circ$ are consecutive interior angles (inside the parallel lines on the same side of the transversal). They add up to $180^\circ$.
* Calculation: $180 - 112 = 68$
* $x = 68$

9.
The angle marked $147^\circ$ and angle $x$ are consecutive interior angles. They add up to $180^\circ$.
* Calculation: $180 - 147 = 33$
* $x = 33$

Final Answer:
1. x = 72°
2. x = 132°
3. x = 60°
4. x = 55°
5. x = 96°
6. x = 105°
7. x = 131°
8. x = 68°
9. x = 33°