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Parallel Lines & Transversals - Worksheet 4 - 10th Grade

Medium

Identify angle pairs formed by parallel lines and a transversal (Medium)

22 problems · 20-25 minutes · Skills: geometry, parallel lines, angles

About This Worksheet

This medium-level worksheet contains 22 problems designed for 10th Grade students practicing parallel lines & transversals. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Parallel lines cut by a transversal is one of the most productive setups in geometry — the angle relationships it creates appear in triangle proofs, polygon angle calculations, and coordinate geometry. Students who master this topic have a powerful set of angle relationships at their disposal for the rest of the course.

  • Identify corresponding, alternate interior, alternate exterior, and co-interior angle pairs
  • Apply parallel line theorems to find unknown angle measures
  • Determine whether two lines are parallel given angle information
  • Write equations using parallel line angle relationships to solve for unknown variables
  • Prove lines are parallel by identifying congruent corresponding or alternate interior angles

How to Solve: Worked Example

Example Problem: Parallel lines cut by a transversal. An angle is 85°. Find its co-interior angle.
Solution Steps:
  1. Co-interior (same-side interior) angles lie between the parallel lines on the same side of the transversal.
  2. They are supplementary, not congruent.
  3. 180 - 85 = 95°.
Answer: 95°
Tip: Most parallel-line pairs are congruent — co-interior is the exception that sums to 180°.
1
Parallel lines are cut by a transversal. An angle measures 63°. Find its linear pair angle.
2
Parallel lines are cut by a transversal. An angle measures 82°. Find its linear pair angle.
3
Parallel lines are cut by a transversal. An angle measures 28°. Find its linear pair angle.
4
Parallel lines are cut by a transversal. An angle measures 25°. Find its co-interior (same-side interior) angle.
5
Parallel lines are cut by a transversal. An angle measures 108°. Find its co-interior (same-side interior) angle.
6
Parallel lines are cut by a transversal. An angle measures 26°. Find its linear pair angle.
7
Parallel lines are cut by a transversal. An angle measures 111°. Find its co-interior (same-side interior) angle.
8
Parallel lines are cut by a transversal. An angle measures 127°. Find its linear pair angle.
9
Parallel lines are cut by a transversal. An angle measures 91°. Find its co-interior (same-side interior) angle.
10
Parallel lines are cut by a transversal. An angle measures 37°. Find its co-interior (same-side interior) angle.
11
Parallel lines are cut by a transversal. An angle measures 87°. Find its co-interior (same-side interior) angle.
12
Parallel lines are cut by a transversal. An angle measures 103°. Find its linear pair angle.
13
Parallel lines are cut by a transversal. An angle measures 63°. Find its co-interior (same-side interior) angle.
14
Parallel lines are cut by a transversal. An angle measures 82°. Find its linear pair angle.
15
Parallel lines are cut by a transversal. An angle measures 47°. Find its linear pair angle.
16
Parallel lines are cut by a transversal. An angle measures 121°. Find its linear pair angle.
17
Parallel lines are cut by a transversal. An angle measures 142°. Find its linear pair angle.
18
Parallel lines are cut by a transversal. An angle measures 26°. Find its linear pair angle.
19
Parallel lines are cut by a transversal. An angle measures 90°. Find its linear pair angle.
20
Parallel lines are cut by a transversal. An angle measures 31°. Find its linear pair angle.
21
Parallel lines are cut by a transversal. An angle measures 131°. Find its linear pair angle.
22
Parallel lines are cut by a transversal. An angle measures 92°. Find its linear pair angle.

Answer Key

1. 117°2. 98°3. 152°4. 155°5. 72°6. 154°7. 69°8. 53°9. 89°10. 143°11. 93°12. 77°13. 117°14. 98°15. 133°16. 59°17. 38°18. 154°19. 90°20. 149°21. 49°22. 88°

Frequently Asked Questions

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What skills does this basics of geometry worksheet cover?

This worksheet focuses on geometry, parallel lines, angles. It is designed for 10th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 22 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.