What defines a complementary angle?

What defines a complementary angle?

• A. Two angles that add up to 180 degrees
• B. Two angles that add up to 90 degrees
• C. Two angles that are equal
• D. Two adjacent angles

Answer: (B)

Two angles that are considered complementary must sum to 90 degrees. This definition is fundamental in geometry. When two angles combine to form a right angle, they are classified as complementary. For instance, if one angle measures 30 degrees, its complementary angle would measure 60 degrees, since 30 + 60 = 90 degrees. This property plays a crucial role in various geometric concepts, including right triangles and trigonometric functions. The other definitions provided do not accurately describe complementary angles. Angles that add up to 180 degrees represent supplementary angles, while equal angles pertain to congruence, and adjacent angles refer to angles that share a common side and vertex but do not inherently have any specific sum relation. Thus, the correct understanding of complementary angles hinges solely on their requirement to total 90 degrees.

Two angles that are considered complementary must sum to 90 degrees. This definition is fundamental in geometry. When two angles combine to form a right angle, they are classified as complementary. For instance, if one angle measures 30 degrees, its complementary angle would measure 60 degrees, since 30 + 60 = 90 degrees. This property plays a crucial role in various geometric concepts, including right triangles and trigonometric functions.

The other definitions provided do not accurately describe complementary angles. Angles that add up to 180 degrees represent supplementary angles, while equal angles pertain to congruence, and adjacent angles refer to angles that share a common side and vertex but do not inherently have any specific sum relation. Thus, the correct understanding of complementary angles hinges solely on their requirement to total 90 degrees.