Geometry worksheet with questions about angle relationships formed by parallel lines and transversals.
A worksheet with geometry problems involving parallel lines and transversals, showing angles and multiple-choice answers.
JPG
1000×1291
57.1 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #611020
⭐
Show Answer Key & Explanations
Step-by-step solution for: Parallel Lines and Transversal worksheet
▼
Show Answer Key & Explanations
Step-by-step solution for: Parallel Lines and Transversal worksheet
Let’s solve each problem one by one. All problems involve parallel lines cut by a transversal, so we’ll use properties of:
- Corresponding angles (equal)
- Alternate interior angles (equal)
- Alternate exterior angles (equal)
- Consecutive interior angles (supplementary — add to 180°)
- Vertical angles (equal)
- Linear pairs (add to 180°)
---
Given: Two parallel lines cut by a transversal. One angle is 58°, and we’re asked for the angle marked with “?” which is vertically opposite to the 58° angle.
✔ Vertical angles are equal.
So, ? = 58°
Answer: C) 58°
---
Given: Two parallel lines cut by a transversal. The top angle is 60°, and we want the angle below it on the other line — this is a corresponding angle.
✔ Corresponding angles are equal → ? = 60°
But wait — let’s double-check the diagram. The 60° is on the top line, and the “?” is on the bottom line, on the same side of the transversal → yes, corresponding.
Answer: C) 60°
---
Given: Two parallel lines cut by a transversal. Angle shown is 54°, and “?” is on the top line, on the opposite side of the transversal → this is an alternate interior angle.
✔ Alternate interior angles are equal → ? = 54°
Answer: D) 54°
---
Given: Two parallel lines cut by a transversal. One angle is 135°, and “?” is on the top line, on the same side as the 135° angle but on the opposite line → this is a consecutive interior angle (also called same-side interior).
✔ Consecutive interior angles are supplementary → ? + 135° = 180°
→ ? = 180° - 135° = 45°
Answer: A) 45°
---
Given: Two parallel lines cut by a transversal. One angle is 109°, and “?” is on the top line, on the same side of the transversal → consecutive interior angle.
✔ Supplementary → ? = 180° - 109° = 71°
Wait — that’s not an option. Let’s re-examine.
Actually, looking at the diagram: the 109° is on the bottom line, and the “?” is on the top line, on the opposite side of the transversal → this is an alternate exterior angle.
✔ Alternate exterior angles are equal → ? = 109°
Answer: D) 109°
---
Given: Two perpendicular lines intersecting — there’s a right angle symbol (90°). The “?” is vertically opposite to the right angle.
✔ Vertical angles are equal → ? = 90°
Answer: D) 90°
---
Given: Two parallel lines cut by a transversal. One angle is 135°, and “?” is on the top line, on the opposite side of the transversal → alternate interior angle.
✔ Alternate interior angles are equal → ? = 135°
Answer: A) 135°
---
Given: Two parallel lines cut by a transversal. One angle is 133°, and “?” is on the bottom line, on the same side of the transversal → consecutive interior angle.
✔ Supplementary → ? = 180° - 133° = 47°
Wait — 47° isn’t an option. Let’s check again.
Actually, looking at the diagram: the 133° is on the top line, and the “?” is on the bottom line, on the opposite side of the transversal → this is an alternate interior angle.
✔ Alternate interior angles are equal → ? = 133°
Answer: A) 133°
---
## ✔ Final Answers:
| Problem | Answer |
|---------|--------|
| 13 | C) 58° |
| 14 | C) 60° |
| 15 | D) 54° |
| 16 | A) 45° |
| 17 | D) 109° |
| 18 | D) 90° |
| 19 | A) 135° |
| 20 | A) 133° |
All answers are based on standard angle relationships with parallel lines and transversals.
- Corresponding angles (equal)
- Alternate interior angles (equal)
- Alternate exterior angles (equal)
- Consecutive interior angles (supplementary — add to 180°)
- Vertical angles (equal)
- Linear pairs (add to 180°)
---
Problem 13
Given: Two parallel lines cut by a transversal. One angle is 58°, and we’re asked for the angle marked with “?” which is vertically opposite to the 58° angle.
✔ Vertical angles are equal.
So, ? = 58°
Answer: C) 58°
---
Problem 14
Given: Two parallel lines cut by a transversal. The top angle is 60°, and we want the angle below it on the other line — this is a corresponding angle.
✔ Corresponding angles are equal → ? = 60°
But wait — let’s double-check the diagram. The 60° is on the top line, and the “?” is on the bottom line, on the same side of the transversal → yes, corresponding.
Answer: C) 60°
---
Problem 15
Given: Two parallel lines cut by a transversal. Angle shown is 54°, and “?” is on the top line, on the opposite side of the transversal → this is an alternate interior angle.
✔ Alternate interior angles are equal → ? = 54°
Answer: D) 54°
---
Problem 16
Given: Two parallel lines cut by a transversal. One angle is 135°, and “?” is on the top line, on the same side as the 135° angle but on the opposite line → this is a consecutive interior angle (also called same-side interior).
✔ Consecutive interior angles are supplementary → ? + 135° = 180°
→ ? = 180° - 135° = 45°
Answer: A) 45°
---
Problem 17
Given: Two parallel lines cut by a transversal. One angle is 109°, and “?” is on the top line, on the same side of the transversal → consecutive interior angle.
✔ Supplementary → ? = 180° - 109° = 71°
Wait — that’s not an option. Let’s re-examine.
Actually, looking at the diagram: the 109° is on the bottom line, and the “?” is on the top line, on the opposite side of the transversal → this is an alternate exterior angle.
✔ Alternate exterior angles are equal → ? = 109°
Answer: D) 109°
---
Problem 18
Given: Two perpendicular lines intersecting — there’s a right angle symbol (90°). The “?” is vertically opposite to the right angle.
✔ Vertical angles are equal → ? = 90°
Answer: D) 90°
---
Problem 19
Given: Two parallel lines cut by a transversal. One angle is 135°, and “?” is on the top line, on the opposite side of the transversal → alternate interior angle.
✔ Alternate interior angles are equal → ? = 135°
Answer: A) 135°
---
Problem 20
Given: Two parallel lines cut by a transversal. One angle is 133°, and “?” is on the bottom line, on the same side of the transversal → consecutive interior angle.
✔ Supplementary → ? = 180° - 133° = 47°
Wait — 47° isn’t an option. Let’s check again.
Actually, looking at the diagram: the 133° is on the top line, and the “?” is on the bottom line, on the opposite side of the transversal → this is an alternate interior angle.
✔ Alternate interior angles are equal → ? = 133°
Answer: A) 133°
---
## ✔ Final Answers:
| Problem | Answer |
|---------|--------|
| 13 | C) 58° |
| 14 | C) 60° |
| 15 | D) 54° |
| 16 | A) 45° |
| 17 | D) 109° |
| 18 | D) 90° |
| 19 | A) 135° |
| 20 | A) 133° |
All answers are based on standard angle relationships with parallel lines and transversals.
Parent Tip: Review the logic above to help your child master the concept of parallel lines and transversals practice worksheet.
