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

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 valid reason from the given list.

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🔷 Section A: State the missing angle and give a reason

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#### 1. Angle a
- Given: 48°
- The two lines are parallel, and the transversal forms a triangle-like shape.
- The angle marked $ a^\circ $ is vertically opposite to the 48° angle (they are formed by intersecting lines).
- 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 the transversal crosses them.
- Angle $ b^\circ $ is on the same side of the transversal as the 52° angle but inside the parallel lines.
- This makes it a co-interior (consecutive interior) angle, which adds up to 180°.

So:
$$
b = 180^\circ - 52^\circ = 128^\circ
$$

✔ 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 transversal forms a "Z" shape with the 65° angle.
- Angle $ c^\circ $ is alternate to the 65° angle (on opposite sides of the transversal, inside the parallel lines).

✔ Angle c: 65°
✔ Reason: It is an alternate angle and therefore equal.

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#### 4. Angle d
- Given: 71°
- The two lines are parallel, and the transversal forms a triangle.
- Angle $ d^\circ $ is corresponding to the 71° angle (same position relative to the parallel lines and transversal).

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

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🔷 Section B: Calculate the missing angle and give a reason

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#### 1. Angle a
- Given: 108°
- The angle $ a^\circ $ is adjacent to the 108° angle on a straight line.
- Angles on a straight line add up to 180°.

So:
$$
a = 180^\circ - 108^\circ = 72^\circ
$$

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

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#### 2. Angle b
- Given: 43°
- The two lines are parallel, and the transversal creates a "Z" shape.
- Angle $ b^\circ $ is alternate to the 43° angle.

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

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#### 3. Angle c
- Given: 114°
- The two lines are parallel, and the transversal crosses them.
- Angle $ c^\circ $ is corresponding to the 114° angle (same side and position).

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

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#### 4. Angle d
- Given: 79°
- The two lines are parallel, and the transversal forms a "U" shape.
- Angle $ d^\circ $ is co-interior (interior) with the 79° angle.
- So they add up to 180°.

$$
d = 180^\circ - 79^\circ = 101^\circ
$$

✔ Angle d: 101°
✔ Reason: It is an interior angle and therefore adds to 180°.

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✔ Final Answers Summary:

#### 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 | 65° | It is an alternate angle and therefore equal. |
| 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 | 101° | It is an interior angle and therefore adds to 180°. |

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