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

Let me work through each problem step by step.

Problem 1:
- Given: 85° angle shown
- Lines A and B are parallel, C is a transversal
- Angle 1 and the 85° angle are vertical angles (opposite angles where lines cross)
- Vertical angles are equal, so Angle 1 = 85°
- Angle 2 and Angle 1 are corresponding angles (same position at different intersections)
- When lines are parallel, corresponding angles are equal
- So Angle 2 = 85°

Wait, let me reconsider the positions more carefully:
- The 85° angle is in the upper right position at the top intersection
- Angle 1 is in the upper left position at the top intersection - these are supplementary (form a straight line together)
- So Angle 1 + 85° = 180°
- Angle 1 = 180° - 85° = 95°
- Angle 2 is in the lower left position at the bottom intersection
- Angle 1 and Angle 2 are alternate interior angles
- Alternate interior angles are equal when lines are parallel
- So Angle 2 = 95°

Problem 2:
- Given: 122° angle shown
- The 122° angle is in the lower right position at the top intersection
- Angle 1 is in the upper left position at the top intersection
- These are vertically opposite to each other? No, they're not directly opposite
- Let me think: 122° and Angle 1 form a linear pair with the angle between them
- Actually, looking at positions: 122° is lower right, Angle 1 is upper left - these are vertical angles!
- So Angle 1 = 122°
- Angle 2 is in the lower left position at the bottom intersection
- Angle 2 and the 122° angle are consecutive interior angles (same side interior angles)
- Consecutive interior angles add up to 180° when lines are parallel
- So Angle 2 + 122° = 180°
- Angle 2 = 180° - 122° = 58°

Problem 3:
- Given: 72° angle shown
- The 72° angle is in the upper right position at the top intersection
- Angle 1 is in the lower right position at the bottom intersection
- These are corresponding angles
- Corresponding angles are equal when lines are parallel
- So Angle 1 = 72°
- Angle 2 is in the lower left position at the bottom intersection
- Angle 2 and Angle 1 form a linear pair (they're on a straight line)
- So Angle 2 + Angle 1 = 180°
- Angle 2 = 180° - 72° = 108°

Problem 4:
- Given: 140° angle shown
- The 140° angle is in the lower right position at the bottom intersection
- Angle 1 is in the upper right position at the top intersection
- These are corresponding angles
- Corresponding angles are equal when lines are parallel
- So Angle 1 = 140°
- Angle 2 is in the lower left position at the bottom intersection
- Angle 2 and the 140° angle form a linear pair
- So Angle 2 + 140° = 180°
- Angle 2 = 180° - 140° = 40°

Let me double-check my answers:

Problem 1:
- 85° given (upper right, top)
- Angle 1 (upper left, top): forms linear pair with 85°, so 180° - 85° = 95° ✓
- Angle 2 (lower left, bottom): alternate interior with Angle 1, so 95° ✓

Problem 2:
- 122° given (lower right, top)
- Angle 1 (upper left, top): vertical angle with 122°, so 122° ✓
- Angle 2 (lower left, bottom): consecutive interior with 122°, so 180° - 122° = 58° ✓

Problem 3:
- 72° given (upper right, top)
- Angle 1 (lower right, bottom): corresponding angle, so 72° ✓
- Angle 2 (lower left, bottom): linear pair with Angle 1, so 180° - 72° = 108° ✓

Problem 4:
- 140° given (lower right, bottom)
- Angle 1 (upper right, top): corresponding angle, so 140° ✓
- Angle 2 (lower left, bottom): linear pair with 140°, so 180° - 140° = 40° ✓

Final Answer:

Problem 1:
Angle 1 = 95°
Angle 2 = 95°

Problem 2:
Angle 1 = 122°
Angle 2 = 58°

Problem 3:
Angle 1 = 72°
Angle 2 = 108°

Problem 4:
Angle 1 = 140°
Angle 2 = 40°