Complementary and Supplementary Angles
What You’ll Learn
Section titled “What You’ll Learn”In this lesson you’ll learn the definitions of complementary and supplementary angles and how to use them to solve for unknown angles.
The Concept
Section titled “The Concept”Two angles can have special relationships based on their sum:
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Complementary angles: Two angles whose measures add up to 90°. If ∠A + ∠B = 90°, then ∠A and ∠B are complementary. Example: 30° and 60° are complementary.
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Supplementary angles: Two angles whose measures add up to 180°. If ∠A + ∠B = 180°, then ∠A and ∠B are supplementary. Example: 110° and 70° are supplementary (they form a straight line).
Important notes:
- Complementary and supplementary angles do not need to be adjacent (next to each other), though they often are.
- If they are adjacent and supplementary, they form a straight line.
- If they are adjacent and complementary, they form a right angle.
Worked Example
Section titled “Worked Example”-
Two angles are complementary. One measures 35°. What is the other?
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Two angles are supplementary. One measures 120°. What is the other?
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∠A and ∠B are adjacent and form a right angle. If ∠A = 28°, what is ∠B?
They are complementary → ∠B = 90° − 28° = 62°.
Real-World Application
Section titled “Real-World Application”Complementary and supplementary angles appear in many practical situations:
- Construction: Walls meeting at a corner usually form a 90° (right) angle. The two angles on either side are complementary if they make up that corner.
- Design: When laying tiles or flooring, angles that add to 180° (supplementary) help create straight edges.
- Navigation: Turning angles on a map or GPS often involve supplementary relationships (turning left then right to go straight).
- Everyday objects: The angles formed by the back and seat of a chair, or the hands of a clock at certain times.
Recognizing these relationships helps you calculate missing angles without measuring everything directly.