Special Cases: Vertical Angles and Complementary/Supplementary Relationships
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 12: Constructions and Scale Drawings) learn special cases of vertical angles: they can only be complementary when both measure exactly 45 degrees, and only supplementary when both measure exactly 90 degrees.
Key Concepts
Vertical angles can be complementary only when both angles measure $45°$, and vertical angles can be supplementary only when both angles measure $90°$.
Common Questions
When can vertical angles be complementary?
Vertical angles are complementary only when both angles measure exactly 45 degrees, because 45 + 45 = 90 degrees.
When can vertical angles be supplementary?
Vertical angles are supplementary only when both measure exactly 90 degrees, because 90 + 90 = 180 degrees. This happens when two perpendicular lines intersect.
Are vertical angles usually complementary or supplementary?
Usually neither. Vertical angles are equal, so their sum is twice the angle measure. They are complementary only at 45 degrees and supplementary only at 90 degrees.
What chapter in Big Ideas Math Advanced 2 covers special cases of vertical angles?
Chapter 12: Constructions and Scale Drawings in Big Ideas Math Advanced 2 (Grade 7) covers special cases of vertical angles with complementary and supplementary relationships.
Why are two 30-degree vertical angles neither complementary nor supplementary?
30 + 30 = 60 degrees (not 90) and (not 180), so they are neither complementary nor supplementary.