Supplementary and Complementary Angles
Supplementary and Complementary Angles is a Grade 8 geometry skill in Saxon Math Course 3, Chapter 6, where students learn that supplementary angles sum to 180 degrees and complementary angles sum to 90 degrees. Students set up and solve equations to find missing angle measures, applying these relationships to parallel lines, transversals, and real-world geometry problems.
Key Concepts
Property Supplementary angles are two angles whose measures total $180^\circ$. Complementary angles are two angles whose measures total $90^\circ$.
Examples A $130^\circ$ angle and a $50^\circ$ angle are supplementary because $130^\circ + 50^\circ = 180^\circ$. A $25^\circ$ angle and a $65^\circ$ angle are complementary because $25^\circ + 65^\circ = 90^\circ$. Adjacent angles on a straight line are always supplementary, like a $120^\circ$ angle and a $60^\circ$ angle.
Explanation Remember this trick: 'S' in Supplementary stands for 'Straight' line ($180^\circ$), and 'C' in Complementary stands for 'Corner' ($90^\circ$). These angle pairs don't even need to be touching! As long as their measures add up to the magic number, they are considered supplementary or complementary. It's all about teamwork and reaching that total!
Common Questions
What are supplementary angles?
Supplementary angles are two angles whose measures add up to 180 degrees. They form a straight line when placed adjacent to each other.
What are complementary angles?
Complementary angles are two angles whose measures add up to 90 degrees. They form a right angle when placed adjacent to each other.
How do you find a missing supplementary angle?
Subtract the known angle from 180 degrees. For example, if one angle is 65 degrees, its supplement is 180 minus 65 = 115 degrees.
How do you find a missing complementary angle?
Subtract the known angle from 90 degrees. For example, if one angle is 34 degrees, its complement is 90 minus 34 = 56 degrees.
Where are supplementary and complementary angles taught in Grade 8?
These angle relationships are covered in Saxon Math Course 3, Chapter 6: Number and Operations and Data Analysis and Probability.