Complementary angles
Complementary angles are two angles whose measures add up to exactly 90 degrees. If one angle measures 35 degrees, its complement is 90 minus 35 = 55 degrees. The two non-right angles in any right triangle are always complementary to each other. This Grade 7 math skill from Saxon Math, Course 2 is foundational for geometry proofs, triangle calculations, and trigonometry — where the relationship between an angle and its complement is central to understanding sine, cosine, and co-function identities.
Key Concepts
Property Two angles whose measures total $90^\circ$ are called complementary angles.
Examples If $\angle A = 35^\circ$, its complement is $90^\circ 35^\circ = 55^\circ$. In a right triangle, the two non right angles are always complementary to each other.
Explanation Complementary angles are partners that form a perfect right angle, just like the corner of a book. If you have one angle, its complement is whatever is needed to reach that neat $90^\circ$ corner. They 'complete' each other by forming a right angle!
Common Questions
What are complementary angles?
Complementary angles are two angles that together measure exactly 90 degrees. Each angle is the complement of the other.
How do I find the complement of an angle?
Subtract the angle's measure from 90 degrees. The complement of a 35-degree angle is 90 - 35 = 55 degrees.
Do complementary angles have to be adjacent?
No, complementary angles do not have to be next to each other. Any two angles that sum to 90 degrees are complementary, whether they share a side or not.
What is the difference between complementary and supplementary angles?
Complementary angles sum to 90 degrees. Supplementary angles sum to 180 degrees. A helpful memory trick: C comes before S, and 90 comes before 180.
When do students learn about complementary angles?
Complementary angles are introduced in Grade 4-5 and reviewed in Grade 7. Saxon Math, Course 2 covers them in Chapter 7 in the context of geometric angle relationships.
How do complementary angles appear in right triangles?
In a right triangle, one angle is exactly 90 degrees. The other two angles must sum to 90 degrees (since all angles in a triangle sum to 180), so they are always complementary.
How do complementary angles connect to trigonometry?
In trigonometry, the sine of an angle equals the cosine of its complement: sin(A) = cos(90 - A). This is why sine and cosine are called co-functions.