Angle Relationships
A free Geometry lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Complementary angles add to 90 degrees, supplementary angles add to 180 degrees, and vertical angles formed by intersecting lines are congruent. In Geometry Foundations, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
What you'll learn
- Identify angle relationships
- Write equations from diagrams
- Solve for missing angle measures
Worked example
Problem. Two supplementary angles measure x and 115 degrees. Find x.
- Supplementary angles add to 180 degrees.
- Write x + 115 = 180.
- Subtract 115 to get x = 65.
- Connect the result back to Angle Relationships so the geometric relationship is explicit.
Answer: 65 degrees
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 38 degrees. What is its measure?
Show solution
- Complementary angles add to 90.
- 90 - 38 = 52.
Answer: 52
2. Two angles add to 180 degrees. What are they called?
Choices: Complementary · Supplementary · Vertical · Adjacent
Show solution
- Supplementary angles add to 180 degrees.
Answer: Supplementary
3. An angle is supplementary to 104 degrees. What is its measure?
Show solution
- 180 - 104 = 76.
Answer: 76
4. Vertical angles measure 4x and 96 degrees. Find x.
Show solution
- Vertical angles are equal.
- 4x = 96.
Answer: 24
5. Angles x and 2x form a straight line. Find x.
Show solution
- x + 2x = 180.
- 3x = 180.
Answer: 60
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