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Parallel Lines Cut By Transversal - Printable Math Worksheets 8th Grade - Wayground

Parallel Lines Cut By Transversal

Orianne Hyppolyte-Glover

Created by Orianne Hyppolyte-Glover

18 questions

8th Grade

Math

Updated Oct 2026

Parallel Lines Cut By Transversal is a Grade 8 mathematics worksheet that helps students identify angle relationships formed when a transversal crosses parallel lines. The 18-item set includes 17 multiple-choice questions and one fill-in-the-blank question covering alternate interior, alternate exterior, corresponding, vertical, and same-side interior angles, along with identifying a transversal and matching corresponding angles. Students also use these relationships to determine unknown angle measures and solve for variables such as x, y, C, and D. The questions ask learners to recognize congruent and noncongruent angle pairs, apply given measures, and select or enter the correct result. This free printable worksheet includes a complete answer key for independent practice, classwork, review, or assessment in Grade 8 geometry.

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Parallel Lines Cut By Transversal

Total questions: 18

Name
Class
Date
1.
Identify each pair of angles.

Identify each pair of angles.

a)

alternate exterior

b)

same-side interior

c)

corresponding

d)

alternate interior

2.
Identify each pair of angles.

Identify each pair of angles.

a)

corresponding

b)

alternate exterior

c)

alternate interior

d)

same-side interior

3.
Identify each pair of angles.

Identify each pair of angles.

a)

vertical

b)

corresponding

c)

alternate exterior

d)

alternate interior

4.
Name the corresponding angle to angle 4.
Name the corresponding angle to angle 4.
a)
angle 8
b)
angle 6
c)
angle 2
d)
angle 5
5.
Find the value of x.
Find the value of x. 
a)
x = 133
b)
x = 47
6.
Find y.
Find y.
a)
50
b)
130
7.

Alternate exterior angles are outside of the parallel lines and on opposite sides of the ...

a)

angle

b)

measurement

c)

transversal

d)

vertex

8.
Which angle is a vertical angle to with ?

Which angle is a vertical angle to with ∠7\angle7  ?

a)

∠1\angle1  

b)

∠5\angle5  

c)

∠3\angle3  

d)

∠6\angle6  

e)

∠9\angle9  

9.
11) Given the two parallel lines cut by a transversal, What is the measure of if ?

11) Given the two parallel lines cut by a transversal,

What is the measure of ∠4\angle4  if  m∠8=76°m\angle8=76\degree  ?



(a)  

10.
Which of these angles is NOT congruent to angle 5?
Which of these angles is NOT congruent to angle 5?
a)
Angle 6
b)
Angle 8
c)
Angle 1
d)
Angle 4
11.
Solve for angle 5
Solve for angle 5
a)
65
b)
60
c)
110
d)
115
12.
A line that passes through parallel lines is called a ______________.
a)
transitive
b)
passer through line
c)
transversal
d)
bisector
13.
Find C
Find C 
a)
∠C=116°
b)
∠C=64°
c)
∠C=180°
d)
∠C=26°
14.
Find D
Find D
a)
∠D=116°
b)
∠D=64°
c)
∠D=180°
d)
∠D=26°
15.
If angle 6 is 25 degrees, how many degrees is angle 7?
If angle 6 is 25 degrees, how many degrees is angle 7?
a)
25 degrees
b)
50 degrees
c)
90 degrees
d)
155 degrees
16.
5) True or False. If the following parallel lines are cut by a transversal, would and be corresponding?

5) True or False.

If the following parallel lines are cut by a transversal, would 
∠2\angle2  and  ∠6\angle6   be corresponding?

a)

True

b)

False

17.
Question Image
a)
55o alternate
b)
55o corresponding
c)
125o alternate
d)
125o corresponding
18.
What are alternate interior angles?

What are alternate interior angles?

a)

A pair of angles on the outer side of two lines cut by a transversal, but on opposite sides of the transversal

b)

The angles opposite of each other when two lines cross

c)

A pair of angles on the inner side of two lines cut by a transversal, but on opposite sides of the transversal

d)

Two angles in the same position when parallel lines are cut by a transversal

WaygroundAnswer Key

Parallel Lines Cut By Transversal

Total questions: 18

1.
d)

alternate interior

2.
b)

alternate exterior

3.
a)

vertical

4.
a) angle 8
5.
a) x = 133
6.
b) 130
7.
c)

transversal

8.
e)

∠9\angle9  

9.
76
10.
a) Angle 6
11.
a) 65
12.
c) transversal
13.
a) ∠C=116°
14.
b) ∠D=64°
15.
d) 155 degrees
16.
b)

False

17.
b) 55o corresponding
18.
c)

A pair of angles on the inner side of two lines cut by a transversal, but on opposite sides of the transversal

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FAQs

What does the Parallel Lines Cut By Transversal worksheet cover?

This Grade 8 worksheet uses 17 multiple-choice questions and one fill-in-the-blank item to assess angle relationships formed by parallel lines and a transversal. Students identify alternate interior, alternate exterior, corresponding, vertical, and same-side interior angles, then use those relationships to find unknown measures and solve for variables such as x, y, C, and D.

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

Introduce the worksheet by reviewing how to locate the two parallel lines, the transversal, and each angle at the intersections. Have students first classify the angle pairs and identify corresponding or vertical partners, then complete the measure-and-variable questions so they apply those relationships rather than rely on visual estimates. Use items involving angles 5, 6, and 7 to prompt students to explain why an angle is congruent to or different from another angle.

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

Students may confuse alternate interior angles with alternate exterior angles by overlooking whether the angles lie between or outside the parallel lines. They may also mix up corresponding and vertical angles, or identify a matching angle without checking its position at the other intersection. In the calculation items, watch for students choosing a nearby-looking measure or failing to use the given angle relationship when solving for x, y, C, or D.

How do I assign and grade the Parallel Lines Cut By Transversal worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for checking the 18 responses. For printable submissions, teachers can scan student work with the Wayground for Teachers app to support grading. The PDF option also gives schools a way to provide geometry practice while reducing screen time.

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

In the worksheet’s Advanced Settings, adjust font spacing and font size to make the angle labels, answer choices, and variable-solving items easier to read. You can also select a dyslexia-friendly font or translate the worksheet into another language when those options support access to the geometry vocabulary and directions.

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 help students build essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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