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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. In Geometry Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

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.
  4. Connect the calculation back to Angle Relationships for Pre-Algebra so the method, not just the arithmetic, is clear.

Answer: 52

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

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

Show solution
  1. Complementary angles add to 90 degrees.
  2. 90 - 35 = 55.

Answer: 55

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

Show solution
  1. Supplementary angles add to 180 degrees.
  2. 180 - 110 = 70.

Answer: 70

3. Vertical angles are always...

Choices: Equal · Complementary · Supplementary · Right angles

Show solution
  1. Vertical angles are opposite angles formed by intersecting lines.
  2. They have equal measure.

Answer: Equal

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

Show solution
  1. Complementary angles add to 90.
  2. 90 - 42 = 48.

Answer: 48

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

Show solution
  1. Write 3x + 60 = 180.
  2. Subtract 60: 3x = 120.
  3. Divide by 3: x = 40.

Answer: 40

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