Parallel and Perpendicular Lines with a Trasnversal Line worksheet ... - Free Printable

Let's solve each of the four problems step by step using the properties of parallel lines and a transversal.

We are told:
- Lines A and B are parallel.
- Line C is a transversal (a line that crosses two or more lines).
- We'll use angle relationships such as:
- Corresponding angles are equal.
- Alternate interior angles are equal.
- Alternate exterior angles are equal.
- Consecutive interior angles (same-side interior) add up to 180°.
- Vertical angles are equal.
- Supplementary angles add up to 180°.

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🔷 Problem 1:

Given:
Angle at the top = 85°
Lines A || B, transversal C

We need to find:
- Angle 1
- Angle 2

Step-by-step:

- The 85° angle and Angle 1 are vertical angles → they are equal.
→ So, Angle 1 = 85°

- Now, Angle 1 and Angle 2 are alternate interior angles (since lines A and B are parallel), so they are equal.
→ Angle 2 = 85°

✔ Answer:
- Angle 1 = 85°
- Angle 2 = 85°

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🔷 Problem 2:

Given:
Angle between transversal and lower line B = 122°
We need to find:
- Angle 1
- Angle 2

Step-by-step:

- The given 122° angle is on line B, and it’s adjacent to Angle 2.
→ They form a straight line → supplementary → sum = 180°
→ So, Angle 2 = 180° – 122° = 58°

- Now, Angle 1 and the 122° angle are corresponding angles (they are in the same relative position at the intersection with A and B).
→ Since A || B, corresponding angles are equal.
→ So, Angle 1 = 122°

✔ Answer:
- Angle 1 = 122°
- Angle 2 = 58°

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🔷 Problem 3:

Given:
Angle at top = 72°
We need to find:
- Angle 1
- Angle 2

Step-by-step:

- The 72° angle and Angle 1 are alternate interior angles (they are on opposite sides of the transversal and inside the parallel lines).
→ So, Angle 1 = 72°

- Now, Angle 1 and Angle 2 are adjacent angles forming a straight line → supplementary.
→ So, Angle 2 = 180° – 72° = 108°

✔ Answer:
- Angle 1 = 72°
- Angle 2 = 108°

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🔷 Problem 4:

Given:
Angle below line B = 140°
We need to find:
- Angle 1
- Angle 2

Step-by-step:

- The 140° angle and Angle 2 are vertical angles → equal.
→ So, Angle 2 = 140°

- Now, Angle 1 and the 140° angle are consecutive interior angles (on the same side of the transversal, between the parallel lines).
→ They are supplementary → sum = 180°
→ So, Angle 1 = 180° – 140° = 40°

✔ Answer:
- Angle 1 = 40°
- Angle 2 = 140°

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✔ Final Answers:

| Problem | Angle 1 | Angle 2 |
|--------|---------|---------|
| 1 | 85° | 85° |
| 2 | 122° | 58° |
| 3 | 72° | 108° |
| 4 | 40° | 140° |

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📌 Summary of Key Concepts Used:

- Vertical angles: Equal
- Corresponding angles: Equal (when lines are parallel)
- Alternate interior angles: Equal
- Same-side interior angles: Add to 180°
- Straight line angles: Add to 180°

Let me know if you'd like a diagram explanation or printable version!