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Two Parallel Lines cut by a Transversal - Printable Math Worksheets 7th - 9th Grade - Wayground

Two Parallel Lines cut by a Transversal

Lauren Pachter

Created by Lauren Pachter

20 questions

7th - 9th Grade

Math

Updated Oct 2026

Two Parallel Lines cut by a Transversal is a free printable mathematics worksheet for students in Grades 7–9. It focuses on identifying transversals and using angle relationships formed by parallel lines, including corresponding, alternate exterior, vertical, congruent, complementary, and supplementary angles. The 20-question worksheet includes 19 multiple-choice items and one multiple-select item. Students determine unknown angle measures, identify relationships, calculate supplements, and solve for variables by setting angle expressions equal or using a supplementary relationship. An answer key is included, making this worksheet useful for guided practice, independent review, or assessment of students’ ability to connect angle diagrams with equations.

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Two Parallel Lines cut by a Transversal

Total questions: 20

Name
Class
Date
1.
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
2.
A line that passes through parallel lines is called a ______________.
a)
vertical lines
b)
a passer through line
c)
transversal
d)
perpendicular line
3.
If m<1 = 27 o Find the m<4
If m<1 = 27o
Find the m<4
a)
27o
b)
153o
c)
63o
d)
90o
4.
If angle P measures 60 degrees, what is the measure of angle C?
If angle P measures 60 degrees, what is the measure of angle C?
a)
60o
b)
30o
c)
120o
d)
180o
5.
If angle P measures 50 degrees, what is the measure of angle Q?
If angle P measures 50 degrees, what is the measure of angle Q?
a)
50o
b)
40o
c)
130o
d)
180o
6.
What is the supplement angle to a 45° angle?
a)
45°
b)
180°
c)
135°
d)
100°
7.
Line m is parallel to line n. Find the measure of ∠1.
Line m is parallel to line n. Find the measure of ∠1.
a)
65°
b)
115°
c)
125°
d)
180°
8.
Angle 1 and 6 are alternate exterior angles, m<1=125 degrees, and m<6 = 5x. Find the value of x.
Angle 1 and 6 are alternate exterior angles, m<1=125 degrees, and m<6 = 5x.  Find the value of x.
a)
125
b)
100
c)
20
d)
25
9.
The two angles that are 75 degrees are an example of...

The two angles that are 75 degrees are an example of...

a)

a linear pair

b)

vertical angles

c)

complementary angles

d)

supplementary angles

10.
Angle 2 and 5 are corresponding angles, m ∠ 2 = 60 ° m\angle2=60\degree m ∠ 2 = 6 0 ° , and m ∠ 5 = ( x + 25 )…

Angle 2 and 5 are corresponding angles,  m∠2=60°m\angle2=60\degree , and  m∠5=(x+25)m\angle5=\left(x+25\right) . Find the value of x.

a)

x=120

b)

x=60

c)

x=45

d)

x=35

11.
Angle 1 and 6 are alternate exterior angles, m ∠ 1 = 125 ° m\angle1\ =\ 125\degree m ∠ 1 = 1 2 5 ° degrees, and m ∠ 6 = 5 x…

Angle 1 and 6 are alternate exterior angles,  m∠1 = 125°m\angle1\ =\ 125\degree   degrees, and  m∠6 = 5xm\angle6\ =\ 5x  . Find the value of x.

a)

125

b)

100

c)

20

d)

25

12.
What is the correct EQUATION to find the value of x AND what is the value of x? (Hint: Check two answers)

What is the correct EQUATION to find the value of x AND what is the value of x? (Hint: Check two answers)

a)

X=12

b)

8X - 17 + 5X +19 = 180

c)

8X - 17 = 5X +19

d)

X= -12

13.
What is the measure of ∠3?
What is the measure of ∠3?
a)
55
b)
155
c)
45
d)
135
14.
Angle 1 = 3x - 4 Angle 3 = 5x - 38 Find the measure of Angle 4
Angle 1 = 3x - 4
Angle 3 = 5x - 38
Find the measure of Angle 4
a)
17o
b)
47o
c)
133o
d)
55o
15.
Question Image
a)
x=29
b)
x=61
c)
x=14
d)
x=20
16.
Find m∠UVY if m∠TWX = 84°
Find m∠UVY if m∠TWX = 84°
a)
80°
b)
84°
c)
74°
d)
110°
17.
Solve for x.
Solve for x.
a)
21
b)
4
c)
8
d)
5
18.
Question Image
a)
x=29
b)
x=61
c)
x=14
d)
x=20
19.
Thanksgiving is only an American holiday.
a)
True
b)
False
20.
What season is Thanksgiving in?
a)
Spring
b)
Summer
c)
Winter
d)
Fall
WaygroundAnswer Key

Two Parallel Lines cut by a Transversal

Total questions: 20

1.
a) Angle 6
2.
c) transversal
3.
a) 27o
4.
c) 120o
5.
c) 130o
6.
c) 135°
7.
b) 115°
8.
d) 25
9.
b)

vertical angles

10.
d)

x=35

11.
d)

25

12.
c)

8X - 17 = 5X +19

, a)

X=12

13.
c) 45
14.
c) 133o
15.
a) x=29
16.
b) 84°
17.
b) 4
18.
a) x=29
19.
a) True
20.
d) Fall

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FAQs

What does the Two Parallel Lines cut by a Transversal worksheet cover?

This worksheet helps Grades 7–9 students identify a transversal and use relationships among angles formed by two parallel lines. Through 19 multiple-choice questions and one multiple-select question, students find unknown measures using corresponding, alternate exterior, vertical, congruent, and supplementary angles, including problems that require solving for x.

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

Introduce the diagram vocabulary by having students identify the transversal, then model how corresponding, alternate exterior, and vertical angles determine whether measures are equal. As students work through the worksheet, ask them to name the relationship before calculating a measure or writing an equation; use the variable problems to connect angle relationships with algebra.

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

Watch for students confusing equal-angle relationships, such as corresponding or alternate exterior angles, with supplementary relationships that total 180°. Students may also choose an angle measure without identifying the relationship first, forget to set expressions equal when angles are congruent, or select only one part of the multiple-select item instead of both the correct equation and the value of x.

How do I assign and grade this parallel-lines worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses from the digital quiz.

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

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the angle diagrams, labels, and multiple-choice options are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when that supports access to the angle-relationship practice.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all 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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