Complementary angles
Complementary angles are two angles whose measures add up to 90 degrees. In Grade 6 Saxon Math Course 1, students find missing complementary angles by subtracting the known angle from 90°. If one angle is 35°, its complement is 90° − 35° = 55°. Complementary angle pairs commonly appear in right triangles, where the two non-right angles are always complementary. This relationship is a foundational geometric tool used in proofs, trigonometry, and construction problems.
Key Concepts
Property Complementary angles are two angles whose measures total $90^\circ$.
Examples An angle of $30^\circ$ and an angle of $60^\circ$ are complementary because $30^\circ + 60^\circ = 90^\circ$. The complement of a $25^\circ$ angle is a $65^\circ$ angle, since $90^\circ 25^\circ = 65^\circ$. If $\angle A$ and $\angle B$ are complementary and $\angle A = 80^\circ$, then $\angle B = 10^\circ$.
Explanation Think of a perfect corner, like on a book, which is a $90^\circ$ angle. If you split that corner into two smaller angles, they 'complement' each other. This means their measures add up to make the full $90^\circ$. They are the dynamic duo of right angles!
Common Questions
What are complementary angles?
Two angles whose measures sum to 90°.
If one angle is 35°, what is its complement?
90° − 35° = 55°.
What angle is its own complement?
45°. A 45° angle is its own complement: 45° + 45° = 90°.
How do complementary angles appear in a right triangle?
The two non-right angles of a right triangle always sum to 90°, making them complementary.
What is the difference between complementary and supplementary angles?
Complementary angles sum to 90°; supplementary angles sum to 180°. Memory tip: C comes before S alphabetically, and 90° < 180°.