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Identify complementary angles

Complementary angles are two angles whose measures add to 90°, so each angle is acute; they may be adjacent or separate, although adjacent complementary angles together form a right angle. The relationship can be identified from angle measures, equations, or diagrams and distinguished from supplementary angles, whose measures add to 180°; trigonometric applications and more advanced generalizations are not included.

Detailed Explanation: Identify complementary angles

Two angles are complementary if their measures add to 90∘90^\circ.

To identify complementary angles:

  1. Add the two angle measures.
  2. If the sum is 90∘90^\circ, the angles are complementary.
  3. Check that both angles are acute, meaning each is less than 90∘90^\circ.

Example: Are angles measuring 38∘38^\circ and 52∘52^\circ complementary?

Add their measures:

38∘+52∘=90∘38^\circ+52^\circ=90^\circ

Because the sum is 90∘90^\circ, the angles are complementary. Both angles are also acute.

Remember: angles that add to 180∘180^\circ are supplementary, not complementary.

Learn by doing: Identify complementary angles

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