Properties of Complementary Angles
Properties of Complementary Angles is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 12: Constructions and Scale Drawings, where students learn that two angles are complementary if their measures sum to 90 degrees, and use this property to find unknown angle measures in geometric figures and real-world diagrams. Complementary angles often appear in right triangles and architectural designs.
Key Concepts
If two angles are complementary, then both angles must be acute angles (less than $90°$).
Common Questions
What are complementary angles?
Two angles are complementary if their measures add up to 90 degrees. For example, a 35-degree angle and a 55-degree angle are complementary because 35 + 55 = 90.
How do you find the complement of an angle?
Subtract the angle from 90 degrees. The complement of a 42-degree angle is 90 - 42 = 48 degrees.
Where do complementary angles appear in geometry?
Complementary angles appear in right triangles (the two acute angles are always complementary), in figures with right-angle corners, and in real-world contexts like ramp inclines and roof angles.
What is Big Ideas Math Advanced 2 Chapter 12 about?
Chapter 12 covers Constructions and Scale Drawings, including angle relationships (complementary, supplementary, vertical), properties of quadrilaterals, geometric constructions, and scale drawings.