Educational worksheet on angles formed by parallel lines, including corresponding, alternate, and interior angles with provided clues.

Let's solve each question in Section A and Section B step by step, using the angle rules for parallel lines. We'll identify the missing angles and provide a correct reason from the given list.

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🔷 Section A

#### 1. Angle a:
- Given: 48°
- The two lines are parallel, and the transversal forms a triangle-like shape.
- The angle `a` is vertically opposite to the 48° angle (they are opposite angles at the intersection).
- So, they are equal.

✔ Angle a: 48°
✔ Reason: It is a vertically opposite angle and therefore equal.

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#### 2. Angle b:
- Given: 52°
- The angle `b` is on the same side of the transversal and between the two parallel lines — it’s an interior angle.
- Since the two lines are parallel, interior angles on the same side add up to 180°.

So:
> b = 180° – 52° = 128°

✔ Angle b: 128°
✔ Reason: It is an interior angle and therefore adds to 180°.

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#### 3. Angle c:
- Given: 65°
- The two lines are parallel, and the angle `c` is on the same side as 65°, but inside the lines — again, this is a pair of interior angles.
- So, they add up to 180°.

> c = 180° – 65° = 115°

✔ Angle c: 115°
✔ Reason: It is an interior angle and therefore adds to 180°.

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#### 4. Angle d:
- Given: 71°
- This is a corresponding angle — it's in the same position relative to the transversal and the parallel lines.
- Corresponding angles are equal when lines are parallel.

✔ Angle d: 71°
✔ Reason: It is a corresponding angle and therefore equal.

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🔷 Section B

#### 1. Angle a:
- Given: 108°
- The angle `a` is on a straight line with the 108° angle, so they form a straight line → sum = 180°

> a = 180° – 108° = 72°

✔ Angle a: 72°
✔ Reason: Angles on a straight line add up to 180°.

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#### 2. Angle b:
- Given: 43°
- Angle `b` is alternate to the 43° angle — it's on the opposite side of the transversal but between the parallel lines.
- Alternate angles are equal.

✔ Angle b: 43°
✔ Reason: It is an alternate angle and therefore equal.

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#### 3. Angle c:
- Given: 114°
- Angle `c` is corresponding to the 114° angle (same position on the transversal across parallel lines).
- Corresponding angles are equal.

✔ Angle c: 114°
✔ Reason: It is a corresponding angle and therefore equal.

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#### 4. Angle d:
- Given: 79°
- Angle `d` is vertically opposite to the 79° angle (they are opposite angles formed by intersecting lines).
- Vertically opposite angles are equal.

✔ Angle d: 79°
✔ Reason: It is a vertically opposite angle and therefore equal.

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✔ Final Answers:

#### Section A
| Angle | Value | Reason |
|-------|-------|--------|
| a | 48° | It is a vertically opposite angle and therefore equal. |
| b | 128° | It is an interior angle and therefore adds to 180°. |
| c | 115° | It is an interior angle and therefore adds to 180°. |
| d | 71° | It is a corresponding angle and therefore equal. |

#### Section B
| Angle | Value | Reason |
|-------|-------|--------|
| a | 72° | Angles on a straight line add up to 180°. |
| b | 43° | It is an alternate angle and therefore equal. |
| c | 114° | It is a corresponding angle and therefore equal. |
| d | 79° | It is a vertically opposite angle and therefore equal. |

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