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Parallel Lines Cut by Two Transversals - Printable Math Worksheets 8th Grade - Wayground

Parallel Lines Cut by Two Transversals

Barbara White

Created by Barbara White

19 questions

8th Grade

Math

Updated Jan 2026

This Grade 8 mathematics worksheet develops students’ ability to analyze angle relationships created when parallel lines are cut by one or two transversals. Students identify alternate interior, alternate exterior, and corresponding angles, determine unknown angle measures, use supplementary relationships, solve for variables in angle expressions, and decide which lines must be parallel from the information shown in diagrams. The 19 questions include 17 multiple-choice items and 2 multiple-select items. Students apply angle relationships to standard line diagrams and a real-world parking-spot context, including finding missing measures such as 68°, 48°, and 88° and solving equations for x. This free printable worksheet is designed for Grade 8 math practice, review, or assessment and includes a complete answer key for checking student work.

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Parallel Lines Cut by Two Transversals

Total questions: 19

Name
Class
Date
1.
Parallel lines s and t are cut by a transversal r . Which angles are alternate exterior angles?

Parallel lines s and t are cut by a transversal r.

Which angles are alternate exterior angles?

a)


∠2 and ∠8\angle2\ and\ \angle8

b)

∠4 and ∠6\angle4\ and\ \angle6

c)

∠1 and ∠5\angle1\ and\ \angle5

d)

∠1 and ∠8\angle1\ and\ \angle8

2.
Parallel lines s and t are cut by a transversal r . Which angles are corresponding angles?

Parallel lines s and t are cut by a transversal r.

Which angles are corresponding angles?

a)


∠3 and ∠7\angle3\ and\ \angle7

b)

∠1 and ∠7\angle1\ and\ \angle7

c)

∠4 and ∠6\angle4\ and\ \angle6

d)

∠1 and ∠8\angle1\ and\ \angle8

3.
Parallel lines r and s are cut by two transversals, parallel lines t and u . Which angles are alternate exterior angles with…

Parallel lines r and s are cut by two transversals, parallel lines t and u.

Which angles are alternate exterior angles with angle 11?

a)


∠5 and ∠13\angle5\ and\ \angle13

b)

∠7 and ∠15\angle7\ and\ \angle15

c)

∠6 and ∠16\angle6\ and\ \angle16

d)

∠8 and ∠14\angle8\ and\ \angle14

4.
Parallel lines r and s are cut by two transversals, parallel lines t and u . Which angles are alternate interior angles with…

Parallel lines r and s are cut by two transversals, parallel lines t and u.

Which angles are alternate interior angles with angle 3?

a)


∠5 and ∠13\angle5\ and\ \angle13

b)

∠7 and ∠15\angle7\ and\ \angle15

c)

∠6 and ∠16\angle6\ and\ \angle16

d)

∠8 and ∠14\angle8\ and\ \angle14

5.

Parallel lines r and s are cut by two transversals, parallel lines t and u.

Which angles are corresponding angles with angle 8?

a)


∠4 and ∠12\angle4\ and\ \angle12

b)

∠2 and ∠10\angle2\ and\ \angle10

c)

∠6 and ∠14\angle6\ and\ \angle14

d)

∠3 and ∠9\angle3\ and\ \angle9

6.
Parallel lines s and t are cut by a transversal, r . If the measure of angle 1 is 68°, what is the measure of angle 5?

Parallel lines s and t are cut by a transversal, r.

If the measure of angle 1 is 68°, what is the measure of angle 5?

a)

22

b)

68

c)

112

d)

158

7.
The diagram below shows several parking spots near the grocery store, formed with three parallel line segments and a…

The diagram below shows several parking spots near the grocery store, formed with three parallel line segments and a transversal.

If the measure of angle 4 is 132°, what is the measure of angle 7?

a)

32

b)

48

c)

132

d)

148

8.
What is the measure of angle 1?

What is the measure of angle 1?

a)

86

b)

88

c)

90

d)

92

9.
Which correctly describes how to determine the measure of angle 1?

Which correctly describes how to determine the measure of angle 1?

a)

The 105° angle and angle 2 are alternate exterior angles so angle 2 must measure 105°. Angles 1 and 2 are supplementary angles so angle 1 must measure 75°.

b)

The 105° angle and angle 2 are corresponding angles so angle 2 must measure 105°. Angles 1 and 2 are supplementary angles so angle 1 must measure 75°.

c)

The 105° angle and angle 2 are alternate exterior angles so angle 2 must measure 75°. Angles 1 and 2 are supplementary angles so angle 1 must measure 105°.

d)

The 105° angle and angle 2 are corresponding angles so angle 2 must measure 75°. Angles 1 and 2 are supplementary angles so angle 1 must measure 105°.

10.
Parallel lines s and t are cut by a transversal, r , as shown. What is the value of x to the nearest whole number?

Parallel lines s and t are cut by a transversal, r, as shown.

What is the value of x to the nearest whole number?

a)

18

b)

20

c)

86

d)

94

11.

Two parallel lines are cut by a transversal. Angle 1 measures (4x + 28)°, and the angle adjacent to the alternate exterior angle with angle 1 measures (14x + 8)°. What is the value of x?

a)

1/2

b)

2

c)

8

d)

12

12.
Parallel lines t and u are cut by two transversals, r and s , which intersect line u at the same point. What is the measure…

Parallel lines t and u are cut by two transversals, r and s, which intersect line u at the same point.

What is the measure of angle 2?

a)

25

b)

42

c)

46

d)

88

13.
Question Image

Which is enough to prove that  s∥t ?Which\ is\ enough\ to\ prove\ that\ \ s\parallel t\ ?  

a)

∠1≅∠3\angle1\cong\angle3  

b)

∠2≅∠8\angle2\cong\angle8  

c)

∠5+∠6=180°\angle5+\angle6=180\degree  

d)

∠1+∠4=180°\angle1+\angle4=180\degree  

14.
Question Image

Which is enough to prove u∥v ?Which\ is\ enough\ to\ prove\ u\parallel v\ ?  

a)

∠2≅∠4\angle2\cong\angle4  

b)

∠4≅∠8\angle4\cong\angle8  

c)

∠6+∠7=180°\angle6+\angle7=180\degree  

d)

∠3+∠4=180°\angle3+\angle4=180\degree  

15.
Which lists all the lines that are parallel to line s ?

Which lists all the lines that are parallel to line s?

a)

only line v

b)

only line t and line v

c)

only line u and line v

d)

only lines t, u, and v

16.
which describes all the lines that must be parallel?

If ∠6≅∠10  and  ∠5≅∠7If\ \angle6\cong\angle10\ \ and\ \ \angle5\cong\angle7  

 which describes all the lines that must be parallel?

a)

Only lines r and s must be parallel.

b)

Only lines t and u must be parallel.

c)

Lines r and s and lines t and u must be parallel.

d)

Neither lines r and s nor lines t and u must be parallel.

17.
which describes all the lines that must be parallel?

If ∠8≅∠10  and ∠1≅∠7If\ \angle8\cong\angle10\ \ and\ \angle1\cong\angle7  

which describes all the lines that must be parallel?

a)

Only lines r and s must be parallel.

b)

Only lines t and u must be parallel.

c)

Lines r and s and lines t and u must be parallel.

d)

Neither lines r and s nor lines t and u must be parallel.

18.
Which lines are parallel? Check all that apply.

Which lines are parallel? Check all that apply.

a)

b∥fb\parallel f

b)

b∥db\parallel d

c)

c∥ec\parallel e

d)

c∥dc\parallel d

e)

d∥fd\parallel f

19.
If x = 10, which lines are parallel? Check all that apply.

If x = 10, which lines are parallel? Check all that apply.

a)


b∥cb\parallel c

b)

b∥db\parallel d

c)

b∥eb\parallel e

d)

c∥dc\parallel d

e)

c∥ec\parallel e

WaygroundAnswer Key

Parallel Lines Cut by Two Transversals

Total questions: 19

1.
a)


∠2 and ∠8\angle2\ and\ \angle8

2.
a)


∠3 and ∠7\angle3\ and\ \angle7

3.
a)


∠5 and ∠13\angle5\ and\ \angle13

4.
a)


∠5 and ∠13\angle5\ and\ \angle13

5.
a)


∠4 and ∠12\angle4\ and\ \angle12

6.
b)

68

7.
b)

48

8.
b)

88

9.
a)

The 105° angle and angle 2 are alternate exterior angles so angle 2 must measure 105°. Angles 1 and 2 are supplementary angles so angle 1 must measure 75°.

10.
a)

18

11.
c)

8

12.
b)

42

13.
b)

∠2≅∠8\angle2\cong\angle8  

14.
b)

∠4≅∠8\angle4\cong\angle8  

15.
c)

only line u and line v

16.
b)

Only lines t and u must be parallel.

17.
c)

Lines r and s and lines t and u must be parallel.

18.
a)

b∥fb\parallel f

, c)

c∥ec\parallel e

19.
a)


b∥cb\parallel c

, b)

b∥db\parallel d

, d)

c∥dc\parallel d

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FAQs

What does the Parallel Lines Cut by Two Transversals worksheet cover?

This Grade 8 worksheet focuses on identifying alternate interior, alternate exterior, and corresponding angles when parallel lines are cut by one or two transversals. Across 19 multiple-choice and multiple-select questions, students use those relationships, supplementary angles, and algebraic expressions to find missing angle measures, solve for x, and determine which lines must be parallel.

How can I use this worksheet to teach angle relationships with parallel lines and transversals?

Introduce the angle-position vocabulary with a labeled diagram, then have students identify the relationship before calculating any measure. Use the worksheet’s two-transversal items to ask students to trace which lines and angles they are comparing, and discuss how a known measure such as 68° or 132° leads to a corresponding, alternate, or supplementary angle. Finish with the equation-based questions so students connect angle relationships to solving for x.

What mistakes should I watch for when students complete this worksheet?

Students may confuse alternate interior, alternate exterior, and corresponding angles by focusing on the angle number instead of each angle’s position relative to the lines and transversal. They may also assume equal measures when the angles are actually supplementary, or choose a line as parallel without checking the relationships shown. In the equation items, watch for students who identify the correct angle relationship but set up or solve the algebraic equation incorrectly.

How do I assign and grade this worksheet?

On Wayground, assign this worksheet as a printable PDF or use it as a digital quiz. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time while students practice angle relationships and transversal problems.

How can I differentiate this parallel-lines worksheet for my students?

Use the worksheet’s Advanced Settings to increase font spacing or font size so the line diagrams, angle labels, and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language, while keeping the same angle-identification and missing-measure questions.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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