Answer:
Complementary Angles and Supplementary Angles: Differences and Definitions
Complementary angles and supplementary angles are two common types of angles in geometry. Although they are related concepts, they have different definitions and properties. Here is a brief explanation of the differences between complementary angles and supplementary angles:
Complementary Angles:
Complementary angles are two angles whose sum is equal to 90 degrees. In other words, when two angles are complementary, they add up to a right angle. Complementary angles are denoted as "∠A" and "∠B", where ∠A + ∠B = 90°.
For example, if one angle measures 30 degrees, the complementary angle would measure 60 degrees, since 30 + 60 = 90. Another example of complementary angles would be 45 degrees and 45 degrees, since 45 + 45 = 90.
Supplementary Angles:
Supplementary angles are two angles whose sum is equal to 180 degrees. In other words, when two angles are supplementary, they add up to a straight angle. Supplementary angles are denoted as "∠C" and "∠D", where ∠C + ∠D = 180°.
For example, if one angle measures 60 degrees, the supplementary angle would measure 120 degrees, since 60 + 120 = 180. Another example of supplementary angles would be 90 degrees and 90 degrees, since 90 + 90 = 180.
Differences:
The main difference between complementary angles and supplementary angles is the sum of their measures. Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees. Another difference is the types of angles that they form. Complementary angles form a right angle, while supplementary angles form a straight angle.
In conclusion, complementary angles and supplementary angles are two common types of angles in geometry. Complementary angles add up to a right angle of 90 degrees, while supplementary angles add up to a straight angle of 180 degrees. Understanding the differences between these types of angles is essential for solving problems in geometry and trigonometry.
Step-by-step explanation: