3-3: Complementary Angles

Key Concept

Two angles are complementary angles if the sum of their measures is 90°.

Complementary angles that are adjacent form a right angle. ∠ AOB and ∠ BOC are complementary adjacent angles.

As the measures of the two angles change, the sum of their measures is still 90°.

Adjacent angles AOB and BOC each measure 45°. Together they form angle AOC which is a right angle.

Suppose two complementary angles are not adjacent. Even though ∠ AOB and angle ∠ BOC are not adjacent, the sum of their measures remains 90° as the measures of the two angles change.

Angles AOB and BOC do not share a vertex or a side. Angle AOB measures 45°. Angle BOC measures 45°.

Part 1

Example Finding Complements of Angles

Draw an adjacent complement for each angle. What is the measure of each complement?

  • a. An angle measuring 80°.

  • b. An angle measuring 30°.

  • c. An angle measuring 45°.

Solution

  • a. An angle of 80° and an adjacent angle together form a right angle. The adjacent angle can be on either side of the 80° angle.

    The measure of the complement is 90° − 80°, or 10°.


End ofPage 101

Table of Contents

Digits, Grade 7, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Expressions, Equations, and Relationships Unit C: Measurement and Geometry Unit D: Proportionality English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties