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

To solve the problems, we need to use the properties of angles formed when a transversal intersects two parallel lines. Specifically, we will use the following angle relationships:

1. Corresponding Angles: Angles that are in the same relative position at each intersection are equal.
2. Alternate Interior Angles: Angles that are on opposite sides of the transversal and inside the parallel lines are equal.
3. Same-Side Interior Angles: Angles that are on the same side of the transversal and inside the parallel lines are supplementary (sum to 180°).
4. Vertical Angles: Angles opposite each other when two lines intersect are equal.

Let's solve each problem step by step.

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Problem 1:

- Given: \( \angle 1 = 85^\circ \)
- Lines A and B are parallel, and C is the transversal.

#### Step 1: Identify \( \angle 1 \)
- \( \angle 1 \) is given as \( 85^\circ \).

#### Step 2: Find \( \angle 2 \)
- \( \angle 2 \) is the alternate interior angle to \( \angle 1 \). Since the lines are parallel, alternate interior angles are equal.
- Therefore, \( \angle 2 = 85^\circ \).

#### Final Answer:
\[
\boxed{85, 85}
\]

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Problem 2:

- Given: \( \angle 1 = 72^\circ \)
- Lines A and B are parallel, and C is the transversal.

#### Step 1: Identify \( \angle 1 \)
- \( \angle 1 \) is given as \( 72^\circ \).

#### Step 2: Find \( \angle 2 \)
- \( \angle 2 \) is the corresponding angle to \( \angle 1 \). Since the lines are parallel, corresponding angles are equal.
- Therefore, \( \angle 2 = 72^\circ \).

#### Final Answer:
\[
\boxed{72, 72}
\]

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Problem 3:

- Given: \( \angle 1 = 122^\circ \)
- Lines A and B are parallel, and C is the transversal.

#### Step 1: Identify \( \angle 1 \)
- \( \angle 1 \) is given as \( 122^\circ \).

#### Step 2: Find \( \angle 2 \)
- \( \angle 2 \) is the same-side interior angle to \( \angle 1 \). Since the lines are parallel, same-side interior angles are supplementary.
- Therefore, \( \angle 2 = 180^\circ - 122^\circ = 58^\circ \).

#### Final Answer:
\[
\boxed{122, 58}
\]

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Problem 4:

- Given: \( \angle 1 = 140^\circ \)
- Lines A and B are parallel, and C is the transversal.

#### Step 1: Identify \( \angle 1 \)
- \( \angle 1 \) is given as \( 140^\circ \).

#### Step 2: Find \( \angle 2 \)
- \( \angle 2 \) is the alternate interior angle to \( \angle 1 \). Since the lines are parallel, alternate interior angles are equal.
- Therefore, \( \angle 2 = 140^\circ \).

#### Final Answer:
\[
\boxed{140, 140}
\]

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Summary of Answers:

1. \( \boxed{85, 85} \)
2. \( \boxed{72, 72} \)
3. \( \boxed{122, 58} \)
4. \( \boxed{140, 140} \)

These solutions use the properties of angles formed by a transversal intersecting parallel lines, ensuring accuracy and clarity.