Complementary & Supplementary Angles
Two special angle partnerships: pairs that sum to 90° and pairs that sum to 180°.
Introduction
Two angles are complementary when they combine to fill a right angle, and supplementary when they form a straight line. These relationships appear in proofs and everyday problem-solving.
Past Knowledge
Angle classification (1.3.1). Angle Addition (1.3.2).
Today's Goal
Identify complementary and supplementary angle pairs and solve for unknowns.
Future Success
Linear pairs (1.3.4), transversal angles (Unit 3), and trig complements (Unit 8).
Key Concepts
Complementary Angles
Two angles whose measures sum to 90°.
Supplementary Angles
Two angles whose measures sum to 180°.
Memory Trick
Complementary → Corner (90°). Supplementary → Straight line (180°).
Important: Complementary and supplementary angles do not have to be adjacent — they just need to sum correctly.
Worked Examples
Finding a Complement
Find the complement of a 37° angle.
Answer: 53°
Algebraic Supplements
Two supplementary angles measure and . Find each angle.
Answer: and
Angle Twice Its Complement
An angle is twice its complement. Find the angle.
Let the angle be . Its complement is .
Answer: 60° (and its complement is 30°).
Common Pitfalls
Mixing Up 90° and 180°
Complementary → 90°. Supplementary → 180°. Use the memory trick: Corner, Straight.
Real-Life Applications
Ramp Design & ADA Compliance
A wheelchair ramp makes a small angle with the ground. The angle between the ramp and the vertical wall is its complement. ADA codes specify maximum slope angles, and complementary angle calculations ensure compliance.
Practice Quiz
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