Unit 4 · Topic 2

Angle Relationships

Overview

Use complementary, supplementary, vertical, and adjacent angles to find unknowns.

Topic 2 of 4~20 min
Next: Circumference & Area of CirclesAll 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.

The key relationships

  1. 1Complementary angles add to 90°.
  2. 2Supplementary angles add to 180°.
  3. 3Vertical angles (across an X) are equal.
  4. 4Adjacent angles share a side and a vertex.
Worked example

Two angles are supplementary. One is 110°. Find the other.

  1. 1Supplementary angles add to 180°.
  2. 2180° - 110° = 70°.

Why this matters

Use complementary, supplementary, vertical, and adjacent angles to find unknowns.

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. The key relationships
  2. Complementary angles add to 90°.
  3. Supplementary angles add to 180°.
  4. Vertical angles (across an X) are equal.
  5. Adjacent angles share a side and a vertex.

Video walkthroughs

Math Antics

Angle Basics

Right, acute, obtuse, complementary, and supplementary angles.

Watch on YouTube
Khan Academy

Vertical Angles Are Equal

Prove and use the fact that vertical angles are congruent.

Watch on YouTube
Khan Academy

Angles, Parallel Lines & Transversals

Identify corresponding and alternate angle relationships.

Watch on YouTube
Khan Academy

Area of an Isosceles Triangle

Use complementary and supplementary angles to find missing measures.

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

Two angles are complementary. One measures 28°. Find the other.

Step-by-step solution

  1. 1Complementary angles sum to 90°.
  2. 290 − 28 = 62°.

Exercise 2

Try it yourself

Two angles are supplementary. One measures 115°. Find the other.

Step-by-step solution

  1. 1Supplementary angles sum to 180°.
  2. 2180 − 115 = 65°.

Exercise 3

Try it yourself

Vertical angles are formed when two lines cross. One angle is 47°. Find its vertical angle.

Step-by-step solution

  1. 1Vertical angles are congruent.
  2. 2The vertical angle is also 47°.

Exercise 4

Try it yourself

An angle is 20° more than its supplement. Find the angle.

Step-by-step solution

  1. 1Let x be the angle; its supplement is 180 − x.
  2. 2The angle is 20° more than its supplement: x = (180 − x) + 20.
  3. 32x = 200, so x = 100°.

Exercise 5

Try it yourself

Two lines intersect. One angle is (3x + 10)° and its vertical angle is (5x − 30)°. Find x.

Step-by-step solution

  1. 1Vertical angles are equal: 3x + 10 = 5x − 30.
  2. 240 = 2x, so x = 20.

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.

Angle Relationships

Question 1 of 4

Easy

An angle is complementary to a 35° angle. What is its measure?

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