Unit 6 · Topic 3

Angles & Parallel Lines

Overview

Find angle measures when a transversal crosses parallel lines.

Topic 3 of 3~54 min
Unit overview

The lesson

This lesson teaches Angles & Parallel Lines. 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

When you study when a transversal crosses parallel lines, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

  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

Angles & Parallel Lines shows up constantly in find angle measures when a transversal crosses parallel lines. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

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 walkthrough

Khan Academy

Angles, Parallel Lines & Transversals

Corresponding and alternate angle relationships.

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°.

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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