If two angles are complements of the same angle, then the two angles are equal.

This is because complementary angles are defined as two angles whose measures add up to 90°. So, if two angles are complements of the same angle, they both satisfy the equation:

$x + y = 90^\circ$

Since both angles add to the same complement, they must be equal.

Would you like more details or have any questions?

Here are five related questions:

1. What does it mean for two angles to be supplementary?
2. Can an obtuse angle have a complement?
3. How do complementary and supplementary angles differ?
4. What are vertical angles, and how are they related to this?
5. If two angles are complements and one angle is 40°, what is the other angle?

Tip: When dealing with angle relationships, always double-check definitions like complementary (90°) and supplementary (180°) to avoid confusion.