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Here is the complete solution for Angles on Parallel Lines (A), broken down by section and diagram, with clear reasoning for each missing angle.

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## 🔷 SECTION A: State the missing angle and give a reason

1. Angle a°

Diagram: Two parallel lines cut by a transversal, forming an “Z” shape (alternate angles).
Given: One angle = 48°
Missing: Angle a° (alternate interior angle)

✔ Angle a: 48°
Reason: Alternate angles are equal when two parallel lines are cut by a transversal.

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2. Angle b°

Diagram: Two parallel lines cut by a transversal, forming an “F” shape (corresponding angles).
Given: One angle = 52°
Missing: Angle b° (corresponding angle below)

✔ Angle b: 52°
Reason: Corresponding angles are equal when two parallel lines are cut by a transversal.

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3. Angle c°

Diagram: Two parallel lines cut by a transversal, forming a “C” shape (co-interior or consecutive interior angles).
Given: One angle = 65°
Missing: Angle c° (co-interior angle)

✔ Angle c: 115°
Reason: Co-interior angles add up to 180° (they are supplementary) when two parallel lines are cut by a transversal.
→ 180° - 65° = 115°

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4. Angle d°

Diagram: Two parallel lines cut by a transversal, forming an “F” shape (corresponding angles), but angle d° is vertically opposite to the corresponding angle.

Given: One angle = 71°
Angle d° is vertically opposite to the corresponding angle of 71° → so it’s also 71°.

✔ Angle d: 71°
Reason: Corresponding angles are equal, and vertically opposite angles are also equal — so angle d° equals the given 71°.

*(Note: You can also say “vertically opposite angles are equal” if you identify that d° is vertically opposite to the corresponding angle — both lead to 71°.)*

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## 🔷 SECTION B: Calculate the missing angle and give a reason

1. Angle a°

Diagram: Two parallel lines cut by a transversal. Given angle = 108° (on top line, above transversal). Angle a° is co-interior with it (on bottom line, same side).

✔ Angle a: 72°
Reason: Co-interior angles are supplementary (add to 180°).
→ 180° - 108° = 72°

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2. Angle b°

Diagram: Two parallel lines cut by a transversal. Given angle = 43° (top right, exterior). Angle b° is alternate to it (bottom left, interior).

✔ Angle b: 43°
Reason: Alternate angles are equal when two parallel lines are cut by a transversal.

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3. Angle c°

Diagram: Two parallel lines cut by a transversal. Given angle = 114° (top left, exterior). Angle c° is co-interior with it (bottom right, interior).

✔ Angle c: 66°
Reason: Co-interior angles are supplementary → 180° - 114° = 66°

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4. Angle d°

Diagram: Two parallel lines cut by a transversal. Given angle = 79° (bottom left, interior). Angle d° is vertically opposite to the corresponding angle of 79° → so it’s also 79°.

✔ Angle d: 79°
Reason: Vertically opposite angles are equal. (Alternatively: Corresponding angles are equal → then vertically opposite → still 79°.)

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## ✔ FINAL ANSWERS SUMMARY:

Section A:

| Angle | Value | Reason |
|-------|-------|--------|
| a | 48° | Alternate angles are equal |
| b | 52° | Corresponding angles are equal |
| c | 115° | Co-interior angles add to 180° |
| d | 71° | Corresponding angles are equal (or vertically opposite) |

Section B:

| Angle | Value | Reason |
|-------|-------|--------|
| a | 72° | Co-interior angles add to 180° |
| b | 43° | Alternate angles are equal |
| c | 66° | Co-interior angles add to 180° |
| d | 79° | Vertically opposite angles are equal |

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Let me know if you’d like diagrams annotated or explanations in simpler terms! 📐✨