This worksheet helps students practice identifying and calculating missing angles formed by parallel lines and a transversal.

Explanation:
We are given several diagrams involving parallel lines cut by transversals. We need to find missing angles using angle relationships:
- Corresponding angles are equal when lines are parallel.
- Alternate interior angles are equal.
- Co-interior (consecutive interior) angles add up to 180°.
- Vertically opposite angles are equal.
- Angles on a straight line add to 180°.

Let’s go through each part carefully.

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Section A

1. Angle a:
Two parallel lines, with a transversal forming a triangle-like shape. The top angle is 48°, and angle *a* is inside the “Z” shape — it's an alternate interior angle to the 48° angle.
So:
a = 48°
Reason: Alternate interior angles are equal when lines are parallel.

2. Angle b:
The 52° angle and angle *b* are on the same side of the transversal, between the parallel lines → they are co-interior angles, so they sum to 180°.
So:
b = 180° − 52° = 128°
Reason: Co-interior angles between parallel lines sum to 180°.

3. Angle c:
The 65° angle and angle *c* are on the same side of the transversal, between parallel lines → again, co-interior angles.
So:
c = 180° − 65° = 115°
Reason: Co-interior angles between parallel lines sum to 180°.

4. Angle d:
The 71° angle and angle *d* are corresponding angles (same position relative to the transversal and parallel lines), so they are equal.
So:
d = 71°
Reason: Corresponding angles are equal when lines are parallel.

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Section B

1. Angle a:
The given angle is 108°, and angle *a* is on the same straight line (adjacent), so they form a linear pair → sum to 180°.
So:
a = 180° − 108° = 72°
Reason: Angles on a straight line add to 180°.

2. Angle b:
The 43° angle and angle *b* are alternate interior angles (inside the “Z” shape between parallels).
So:
b = 43°
Reason: Alternate interior angles are equal when lines are parallel.

3. Angle c:
The 114° angle and angle *c* are corresponding angles (both on the same side of the transversal, same relative position), so they are equal.
So:
c = 114°
Reason: Corresponding angles are equal when lines are parallel.

4. Angle d:
The 79° angle and angle *d* are on the same side of the transversal, between the parallel lines → co-interior angles, so they sum to 180°.
So:
d = 180° − 79° = 101°
Reason: Co-interior angles between parallel lines sum to 180°.

Let me double-check all:

- a = 48° ✔️
- b = 128° ✔️
- c = 115° ✔️
- d = 71° ✔️
- Section B: a = 72° ✔️, b = 43° ✔️, c = 114° ✔️, d = 101° ✔️

All consistent.

Final Answer:
Angle a (Sec A): 48°
Angle b (Sec A): 128°
Angle c (Sec A): 115°
Angle d (Sec A): 71°
Angle a (Sec B): 72°
Angle b (Sec B): 43°
Angle c (Sec B): 114°
Angle d (Sec B): 101°