Worksheets · Geometry

Parallel lines and transversals worksheet

When a line crosses two parallel lines, the angles it makes come in pairs. Corresponding, alternate interior and alternate exterior pairs are equal. Co-interior pairs, the ones on the same side of the transversal and between the parallels, add to 180. So does a linear pair, two angles side by side on one line.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Parallel Lines and Transversals

Date Period

Find each measure, or name each pair.

  1. Find angles formed by a transversal

    The lines are parallel. Find x.x50°
  2. In the figure, m∠1=144∘. Find m∠2.12345678
  3. Angle 3 measures 60∘. Find m∠6.12345678
  4. Given m∠8=150∘, find m∠7.12345678

  1. Name the angle pair

    What kind of angle pair are ∠4 and ∠6?12435687
  2. Two lines are cut by a transversal. Which kind of pair are ∠6 and ∠8?56871243
  3. Name the angle pair: ∠2 and ∠7.65782134
  4. Two lines are cut by a transversal. Which kind of pair are ∠1 and ∠5?56781234

  1. Find xx so the lines are parallel

    Two same-side interior angles measure (3x+24)∘ and (6x+39)∘. Find x so that ℓ∥m, and give each angle.
  2. Two alternate interior angles measure (5x−25)∘ and (7x−65)∘. Find x so that ℓ∥m.
  3. Two alternate exterior angles measure (8x−7)∘ and (7x+12)∘. Find x so that ℓ∥m.
  4. Two alternate interior angles measure (7x+27)∘ and (5x+49)∘. Find x so that ℓ∥m, and give each angle.

  1. Find xx and yy with parallel lines

    Lines ℓ and m are parallel. Two corresponding angles measure (4x+36)∘ and (7x−9)∘. The angle that is vertical to the (4x+36)∘ angle measures (5y−14)∘. Find x and y.
  2. Lines ℓ and m are parallel. Two alternate exterior angles measure (3x+12)∘ and (4x−4)∘. The angle that forms a linear pair with the (3x+12)∘ angle measures (2y−6)∘. Find x and y.
  3. Lines ℓ and m are parallel. Two corresponding angles measure (7x−2)∘ and (6x+9)∘. The angle that is vertical to the (7x−2)∘ angle measures (3y+18)∘. Find x and y.
  4. Lines ℓ and m are parallel. Two alternate exterior angles measure (8x+14)∘ and (4x+54)∘. The angle that forms a linear pair with the (8x+14)∘ angle measures (2y+4)∘. Find x and y.

  1. Solve for xx from the drawing

    Find x.(6x + 38)°(x + 114)°
  2. Find x.(4x + 34)°(x + 111)°
  3. Find x, then the measure of the angle marked (5x−10)∘.(5x − 10)°(4x − 1)°
  4. Find x, then the measure of the angle marked (4x+28)∘.(4x + 28)°(x + 122)°

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Parallel Lines and TransversalsAnswer keyVersion 1

Date Period

Find each measure, or name each pair.

  1. Find angles formed by a transversal

    The lines are parallel. Find x.x50°x=130∘
  2. In the figure, m∠1=144∘. Find m∠2.1234567836∘
  3. Angle 3 measures 60∘. Find m∠6.1234567860∘
  4. Given m∠8=150∘, find m∠7.1234567830∘

  1. Name the angle pair

    What kind of angle pair are ∠4 and ∠6?12435687Alternate interior
  2. Two lines are cut by a transversal. Which kind of pair are ∠6 and ∠8?56871243Vertical
  3. Name the angle pair: ∠2 and ∠7.65782134Same-side interior
  4. Two lines are cut by a transversal. Which kind of pair are ∠1 and ∠5?56781234Corresponding

  1. Find xx so the lines are parallel

    Two same-side interior angles measure (3x+24)∘ and (6x+39)∘. Find x so that ℓ∥m, and give each angle.x=13; 63∘ and 117∘
  2. Two alternate interior angles measure (5x−25)∘ and (7x−65)∘. Find x so that ℓ∥m.x=20
  3. Two alternate exterior angles measure (8x−7)∘ and (7x+12)∘. Find x so that ℓ∥m.x=19
  4. Two alternate interior angles measure (7x+27)∘ and (5x+49)∘. Find x so that ℓ∥m, and give each angle.x=11; 104∘ and 104∘

  1. Find xx and yy with parallel lines

    Lines ℓ and m are parallel. Two corresponding angles measure (4x+36)∘ and (7x−9)∘. The angle that is vertical to the (4x+36)∘ angle measures (5y−14)∘. Find x and y.x=15, y=22
  2. Lines ℓ and m are parallel. Two alternate exterior angles measure (3x+12)∘ and (4x−4)∘. The angle that forms a linear pair with the (3x+12)∘ angle measures (2y−6)∘. Find x and y.x=16, y=63
  3. Lines ℓ and m are parallel. Two corresponding angles measure (7x−2)∘ and (6x+9)∘. The angle that is vertical to the (7x−2)∘ angle measures (3y+18)∘. Find x and y.x=11, y=19
  4. Lines ℓ and m are parallel. Two alternate exterior angles measure (8x+14)∘ and (4x+54)∘. The angle that forms a linear pair with the (8x+14)∘ angle measures (2y+4)∘. Find x and y.x=10, y=41

  1. Solve for xx from the drawing

    Find x.(6x + 38)°(x + 114)°x=4
  2. Find x.(4x + 34)°(x + 111)°x=7
  3. Find x, then the measure of the angle marked (5x−10)∘.(5x − 10)°(4x − 1)°x=9, 35∘
  4. Find x, then the measure of the angle marked (4x+28)∘.(4x + 28)°(x + 122)°x=6, 52∘

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Two parallel lines are cut by a transversal. One angle measures 65∘. Find its co-interior angle

  1. Co-interior angles add to 180.
  2. 180 minus 65.

The answer is 115∘.

Where students go wrong

Assuming every pair is equal. Corresponding, alternate interior and alternate exterior angles are; co-interior angles and linear pairs add to 180 instead. If your two angles are on the same side of the transversal and between the parallel lines, they are supplementary, not equal.

Also called transversal angles, corresponding angles, alternate interior angles or co-interior angles.

What you can put on this worksheet

With a diagram, angles numbered 1 to 8
Given m∠5=150∘, find m∠6. — two parallel lines cut by a transversal, with the eight angles numbered 1 to 8 → 30∘
Without a diagram, described in words
Two parallel lines are cut by a transversal. One angle measures 55∘. Find its alternate exterior angle. → 55∘
Without a diagram, solve for x
Two parallel lines are cut by a transversal. A pair of alternate exterior angles measure 2x+104 and 3x+96. Find x. → 8
Are the lines parallel
Can you conclude that ℓ∥m? Explain why or why not. The figure is not drawn to scale. — two lines cut by a transversal, two angles labeled, labeled ℓ, m → No: 135° and 129° are not equal
Name the angle pair
Two lines are cut by a transversal. Which kind of pair are ∠4 and ∠1? — two parallel lines cut by a transversal, with the eight angles numbered 1 to 8 → Vertical
The x that makes the lines parallel
Two alternate interior angles measure (5x+4)∘ and (6x−1)∘. Find x so that ℓ∥m. → x=5
Two unknowns, x and y
Lines ℓ and m are parallel. Two alternate exterior angles measure (6x−2)∘ and (5x+6)∘. The angle that is vertical to the (6x−2)∘ angle measures 2y∘. Find x and y. → x=8, y=23
Solve for x from the drawing
Find x. — two parallel lines cut by a transversal, with angles marked → x=4
Name the pair when there are two transversals
Name the relationship between ∠8 and ∠16. — two parallel lines cut by two transversals, with numbered angles → Corresponding angles
Solve for x with a second transversal in the way
The two horizontal lines are parallel. m∠16=61∘, m∠5=(2x+47)∘, m∠3=(4x+31)∘. Find x. — two parallel lines cut by two transversals, with numbered angles → 8

Questions about these worksheets

Yes. Every parallel lines and transversals sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the parallel lines and transversals questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 10: with a diagram, angles numbered 1 to 8, without a diagram, described in words, without a diagram, solve for x, are the lines parallel, name the angle pair, the x that makes the lines parallel, two unknowns, x and y, solve for x from the drawing, name the pair when there are two transversals and solve for x with a second transversal in the way. Tick as many as you want and set how many of each, or let it spread them evenly.

Assuming every pair is equal. Corresponding, alternate interior and alternate exterior angles are; co-interior angles and linear pairs add to 180 instead. If your two angles are on the same side of the transversal and between the parallel lines, they are supplementary, not equal.