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 that:
- Lines A and B are parallel.
- Line C is a transversal, meaning it crosses both parallel lines.

Key Angle Properties:

1. Corresponding angles are equal.
2. Alternate interior angles are equal.
3. Alternate exterior angles are equal.
4. Consecutive interior angles (same-side interior) add up to 180°.
5. Vertical angles are equal.
6. Linear pairs (adjacent angles on a straight line) add up to 180°.

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Problem 1:

Given:
- Angle adjacent to angle 1 = 85°
- This 85° angle and angle 1 are vertical angles → so they are equal.

So, Angle 1 = 85°

Now, angle 1 and angle 2 are consecutive interior angles (on the same side of transversal C), so they should add to 180°.

→ Angle 2 = 180° - 85° = 95°

✔ Answer:
- Angle 1 = 85°
- Angle 2 = 95°

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Problem 2:

Given:
- One angle is 122°, and it’s between line B and transversal C.

This 122° angle and angle 2 are vertical angles → so angle 2 = 122°

Now, angle 1 and this 122° angle are corresponding angles (they are in the same relative position at each intersection), so:

→ Angle 1 = 122°

Alternatively, angle 1 and angle 2 are alternate interior angles, so they are equal → also confirms angle 1 = 122°

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

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Problem 3:

Given:
- A 72° angle is formed where transversal C intersects line A.

This 72° angle and angle 1 are vertical angles → so angle 1 = 72°

Now, angle 2 and angle 1 are alternate interior angles → so angle 2 = 72°

Alternatively, angle 2 and the 72° angle are corresponding angles — also equal.

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

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Problem 4:

Given:
- An angle of 140° is shown below line B and transversal C.

This 140° angle and angle 2 are vertical angles → so angle 2 = 140°

Now, angle 1 and angle 2 are consecutive interior angles (on the same side of the transversal), so they must add to 180°:

→ Angle 1 = 180° - 140° = 40°

Alternatively, angle 1 and the 140° angle are supplementary because they form a linear pair on a straight line.

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

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Final Answers:

| Problem | Angle 1 | Angle 2 |
|--------|---------|---------|
| 1 | 85° | 95° |
| 2 | 122° | 122° |
| 3 | 72° | 72° |
| 4 | 40° | 140° |

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Summary of Concepts Used:

- Vertical angles = equal
- Corresponding angles = equal (when lines are parallel)
- Alternate interior angles = equal
- Consecutive interior angles = supplementary (add to 180°)

Let me know if you'd like a diagram explanation or more practice!