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Angle Relationships for Pre-Algebra

A free Pre-Algebra lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.

Angle relationships turn geometry into equations. Complementary angles add to 90 degrees, supplementary angles add to 180 degrees, and vertical angles are equal. These facts help solve for missing measures.

What you'll learn

Why it matters: Folded paper crafts, bike spoke patterns, billiards angles, and roof construction all use angle pairs. Vertical, supplementary, and complementary rules let you find an unknown angle without measuring.

Worked example

Problem. An angle is supplementary to 128 degrees. What is its measure?

  1. Supplementary angles add to 180 degrees.
  2. Write x + 128 = 180.
  3. Subtract 128 to get x = 52.

Answer: 52

Practice problems

1. An angle is complementary to 35 degrees. What is its measure?

Show solution
  1. Warm-up: First identify exactly what the question is asking: An angle is complementary to 35 degrees. What is its measure?
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Complementary angles add to 90 degrees.
  4. 90 - 35 = 55.
  5. Check the result by substituting or estimating: the response should match 55 and make sense in the original problem.

Answer: 55

2. An angle is supplementary to 110 degrees. What is its measure?

Show solution
  1. Warm-up: First identify exactly what the question is asking: An angle is supplementary to 110 degrees. What is its measure?
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Supplementary angles add to 180 degrees.
  4. 180 - 110 = 70.
  5. Check the result by substituting or estimating: the response should match 70 and make sense in the original problem.

Answer: 70

3. Vertical angles are always...

Choices: Equal · Complementary · Supplementary · Right angles

Show solution
  1. Warm-up: First identify exactly what the question is asking: Vertical angles are always...
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Vertical angles are opposite angles formed by intersecting lines.
  4. They have equal measure.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Equal

4. Two complementary angles are 42 degrees and x degrees. Find x.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Two complementary angles are 42 degrees and x degrees. Find x.
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Complementary angles add to 90.
  4. 90 - 42 = 48.
  5. Check the result by substituting or estimating: the response should match 48 and make sense in the original problem.

Answer: 48

5. Two supplementary angles are 3x degrees and 60 degrees. Find x.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Two supplementary angles are 3x degrees and 60 degrees. Find x.
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Write 3x + 60 = 180.
  4. Subtract 60: 3x = 120.
  5. Divide by 3: x = 40.
  6. Check the result by substituting or estimating: the response should match 40 and make sense in the original problem.

Answer: 40

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