Skill: Identify complementary angles

Explanation and Free Practice Resources

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.

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Detailed Explanation: Identify complementary angles

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

To identify complementary angles:

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

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

Add their measures:

38^\circ+52^\circ=90^\circ

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

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

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