StudyWiz home
Sign inStart free

Angles and parallel lines worksheet

Grade 8 math, Common Core 8.G.A.5. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

NameDate

Angles and parallel lines

Grade 8 math, Common Core 8.G.A.5

Two parallel lines are cut by a transversal. Find each angle or the value of x.

  1. 1.
    Same-side interior angles measure (4x − 8)° and (2x + 8)°. Find x.
  2. 2.
    One angle measures 40°. What is the measure of its alternate exterior angle?
  3. 3.
    One angle measures 128°. What is the measure of its vertical angle?
  4. 4.
    One angle measures 121°. What is the measure of its corresponding angle?
  5. 5.
    One angle measures 114°. What is the measure of its alternate exterior angle?
  6. 6.
    One angle measures 66°. What is the measure of its same-side interior angle?
  7. 7.
    One angle measures 27°. What is the measure of its angle next to it on the same line?
  8. 8.
    Corresponding angles measure (2x − 4)° and 60°. Find x.
  9. 9.
    One angle measures 108°. What is the measure of its alternate interior angle?
  10. 10.
    Corresponding angles measure (5x + 6)° and 136°. Find x.
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Angles and parallel lines

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. x = 30

    4x − 8 + 2x + 8 = 1806x = 180x = 30

  2. 2. 40°

    These angles are equal

  3. 3. 128°

    These angles are equal

  4. 4. 121°

    These angles are equal

  5. 5. 114°

    These angles are equal

  6. 6. 114°

    These angles add to 180°: 180 − 66 = 114

  7. 7. 153°

    These angles add to 180°: 180 − 27 = 153

  8. 8. x = 32

    2x − 4 = 60x = 32

  9. 9. 108°

    These angles are equal

  10. 10. x = 26

    5x + 6 = 136x = 26

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About angles and parallel lines

When a transversal crosses two parallel lines, it makes eight angles in two matching groups. Corresponding angles, alternate interior angles and alternate exterior angles are equal. Same-side interior angles add up to 180°, and so do angles that form a straight line.

Worked example 1

Corresponding angles measure (3x + 4)° and 61°. Find x.
  1. Step 1.3x + 4 = 61
  2. Step 2.x = 19

Answer: x = 19

Worked example 2

One angle measures 125°. What is the measure of its alternate exterior angle?
  1. Step 1.These angles are equal

Answer: 125°

Worked example 3

Same-side interior angles measure (x + 11)° and (x + 23)°. Find x.
  1. Step 1.x + 11 + x + 23 = 180
  2. Step 2.2x + 34 = 180
  3. Step 3.x = 73

Answer: x = 73

Watch out for

  • Equal pairs: corresponding, alternate interior, alternate exterior and vertical angles.
  • Pairs that add to 180°: same-side interior angles and angles on a straight line.
  • Every angle is either equal to the one you know, or 180° minus it.

Practice angles and parallel lines online

On StudyWiz, your kid can practice angles and parallel lines with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

More grade 8 math worksheets

More from Geometry:

Other grade 8 topics:

See all 8th grade math worksheets, or switch to grade 6 or grade 7.

Keep reading

Try Wiz with tonight’s homework

Free to start, no card needed. Each kid gets 3 homework questions, 5 practice quizzes and 1 writing review a day on the free plan.

Start freeSee pricing