Unit 6 · Topic 3

Angles & Parallel Lines

Overview

Find angle measures when a transversal crosses parallel lines.

Topic 3 of 3~20 min
All units
Unit overview

The lesson

Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

When a transversal crosses parallel lines

  1. 1Corresponding angles are equal.
  2. 2Alternate interior angles are equal.
  3. 3Same-side interior angles are supplementary (add to 180°).
Worked example

Two parallel lines are cut by a transversal. One angle is 65°. Find its corresponding angle.

  1. 1Corresponding angles are equal.
  2. 2So the corresponding angle is also 65°.

Why this matters

Find angle measures when a transversal crosses parallel lines.

These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.

Common mistakes to avoid

Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.

Re-reading the question too quickly. Underline what you are solving for before you start calculating.

Key ideas from this lesson

  1. When a transversal crosses parallel lines
  2. Corresponding angles are equal.
  3. Alternate interior angles are equal.
  4. Same-side interior angles are supplementary (add to 180°).

Video walkthroughs

Khan Academy

Angles, Parallel Lines & Transversals

Corresponding and alternate angle relationships.

Watch on YouTube
Khan Academy

Vertical Angles Are Equal

Use vertical angle relationships with parallel lines.

Watch on YouTube
Math Antics

Angle Basics

Review complementary, supplementary, and angle types.

Watch on YouTube
Khan Academy

Area of an Isosceles Triangle

Apply angle facts to find missing measures in triangles.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

Parallel lines are cut by a transversal. A corresponding angle measures 48°. Find the other corresponding angle.

Step-by-step solution

  1. 1Corresponding angles match in measure.
  2. 2The paired corresponding angle is also 48°.
  3. 3Answer: 48°.

Exercise 2

Try it yourself

Two parallel lines and a transversal form an alternate interior angle of 72°. Find the other alternate interior angle.

Step-by-step solution

  1. 1Alternate interior angles are congruent.
  2. 2The other angle is 72°.
  3. 3Answer: 72°.

Exercise 3

Try it yourself

Same-side interior angles measure 115° and x° with parallel lines. Find x.

Step-by-step solution

  1. 1They add to 180°: 115 + x = 180.
  2. 2x = 65.
  3. 3x = 65°.

Exercise 4

Try it yourself

In a triangle, two angles are 35° and 65°. Find the third angle.

Step-by-step solution

  1. 135 + 65 = 100.
  2. 2180 − 100 = 80.
  3. 3Third angle: 80°.

Exercise 5

Try it yourself

An exterior angle of a triangle is 120°. The two remote interior angles are 50° and x°. Find x.

Step-by-step solution

  1. 1120 = 50 + x.
  2. 2x = 70.
  3. 3x = 70°.

Re-read the lesson section if you get stuck, then try again without peeking at the solution.

Khan Academy

Angle relationships

Open resource
Math Worksheets 4 Kids

Angles worksheets

Open resource

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Angles & Parallel Lines

Question 1 of 4

Medium

Parallel lines are cut by a transversal. An angle measures 110°. Its alternate interior angle is:

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