Find the angle which is equal to its complement

Concept: Two angles are complementary when the sum of their measures is 90°. If one angle measures x, its complement measures (90° − x).

Application:

1. Let the required angle be x, so its complement is (90° − x).

2. The angle is equal to its complement, so x = 90° − x.

3. Adding x to both sides gives 2x = 90°.

4. Dividing both sides by 2 gives x = 45°.

Cross-check: the complement of 45° is 90° − 45° = 45°, which equals the angle itself, confirming the two angles are equal and add up to 90°.