Angles on Parallel Lines (A) (With Clues) Worksheet | Cazoom Maths ... - Free Printable

Let's solve each question step by step using the properties of angles on parallel lines.

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Section A

#### 1. Angle a:
- Given: 48°
- The two lines are parallel, and the angle is formed with a transversal.
- Angle `a` is vertically opposite to the 48° angle (they are directly across from each other at the intersection).
- Vertically opposite angles 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 two lines are parallel, and a transversal cuts them.
- Angle `b` is on the same side of the transversal but inside the parallel lines — this is a corresponding angle.
- Corresponding angles are equal when lines are parallel.

✔ Angle b: 52°
✔ Reason: It is a corresponding angle and therefore equal.

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#### 3. Angle c:
- Given: 65°
- The two lines are parallel, and the angle is between them.
- The 65° angle and angle `c` are interior angles on the same side of the transversal.
- Interior angles on the same side add up to 180°.

So:
> 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°
- The two lines are parallel, and the transversal forms an angle.
- Angle `d` is alternate to the 71° angle (it’s on the opposite side of the transversal and between the lines).
- Alternate angles are equal.

✔ Angle d: 71°
✔ Reason: It is an alternate angle and therefore equal.

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Section B

#### 5. Angle a:
- Given: 108°
- The two lines are parallel, and a transversal crosses them.
- Angle `a` is adjacent to the 108° angle on a straight line.
- Angles on a straight line add up to 180°.

So:
> a = 180° – 108° = 72°

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

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#### 6. Angle b:
- Given: 43°
- The two lines are parallel, and the transversal forms an angle.
- Angle `b` is corresponding to the 43° angle (same position relative to the transversal and parallel lines).
- Corresponding angles are equal.

✔ Angle b: 43°
✔ Reason: It is a corresponding angle and therefore equal.

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#### 7. Angle c:
- Given: 114°
- The two lines are parallel, and a transversal cuts through them.
- Angle `c` is alternate to the 114° angle (on opposite sides of the transversal, inside the parallel lines).
- Alternate angles are equal.

✔ Angle c: 114°
✔ Reason: It is an alternate angle and therefore equal.

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#### 8. Angle d:
- Given: 79°
- The two lines are parallel, and a transversal crosses them.
- Angle `d` is vertically opposite to the 79° angle.
- 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 | 52° | It is a corresponding angle and therefore equal. |
| c | 115° | It is an interior angle and therefore adds to 180°. |
| d | 71° | It is an alternate angle and therefore equal. |

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

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