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What is a characteristic of complementary angles?

  1. They sum to 180 degrees

  2. They sum to 90 degrees

  3. They are equal in measure

  4. They are both obtuse angles

The correct answer is: They sum to 90 degrees

Complementary angles are defined specifically by the sum of their measures. When two angles are considered complementary, their measures always add up to exactly 90 degrees. For example, if one angle measures 30 degrees, the complementary angle would measure 60 degrees because 30 + 60 = 90. Understanding complementary angles is important in geometry, particularly when solving problems involving right triangles or constructing angle relationships. This definition contrasts other options presented, such as angles summing to 180 degrees, which pertains to supplementary angles instead. Similarly, while complementary angles can indeed be equal in measure (like two 45-degree angles), it is not a defining characteristic, as they can also be different measures that still add up to 90 degrees. Lastly, complementary angles are not restricted to obtuse angles; in fact, both angles must be acute (less than 90 degrees) in order to satisfy the condition of being complementary.