Answer:
Complementary and supplementary angles are pairs of angles that have specific relationships to each other when they are combined. These relationships are commonly encountered in geometry and can help us solve various types of problems involving angles. Let's delve into the details of complementary and supplementary angles:
Complementary Angles:
Definition: Complementary angles are a pair of angles whose measures add up to 90 degrees.
Symbol: Complementary angles are often represented as angle "A" and angle "B," and their relationship is written as: A + B = 90°.
Example: If one angle measures 30 degrees, the other complementary angle will measure 60 degrees because 30 + 60 = 90.
Supplementary Angles:
Definition: Supplementary angles are a pair of angles whose measures add up to 180 degrees.
Symbol: Supplementary angles are often represented as angle "X" and angle "Y," and their relationship is written as: X + Y = 180°.
Example: If one angle measures 120 degrees, the other supplementary angle will measure 60 degrees because 120 + 60 = 180.
Key Points:
Right Angle: Complementary angles can be thought of as two angles that make up a right angle, which is 90 degrees.
Straight Line: Supplementary angles can be thought of as two angles that make up a straight line, which is 180 degrees.
Examples: Common examples of complementary angles are 30° and 60°, 45° and 45°, or 20° and 70°. Common examples of supplementary angles are 120° and 60°, 90° and 90°, or 40° and 140°.
Use in Problem Solving: Complementary and supplementary angles often come up when solving geometric problems or working with angles in real-world situations. They are particularly useful in problems involving right angles, straight lines, and angles in various shapes.
Complementary and Supplementary Theorems: These angle relationships are also used in theorems and proofs in geometry to demonstrate various geometric properties.
In summary, complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees. Understanding these angle relationships is fundamental in geometry and is essential for solving a wide range of geometric problems and proofs.
Explanation: