The Complementary Angle Calculator is a simple tool that helps determine the missing angle that, when added to a given angle, equals 90 degrees. In geometry, two angles are said to be complementary if their sum is exactly 90°. This calculator is widely used in mathematics, trigonometry, and geometry to solve angle-related problems quickly and accurately.
For students, teachers, and professionals, the Complementary Angle Calculator eliminates manual calculations, providing instant results for educational and practical purposes.
Formula of Complementary Angle Calculator
The formula to calculate the complementary angle is:
Complementary Angle = 90° – Given Angle
Where:
- Complementary Angle: The missing angle that, when added to the given angle, equals 90°.
- Given Angle: The known angle provided in the problem.
Key Insight:
If the given angle is greater than 90°, it does not have a complementary angle because complementary angles only apply to angles that sum to exactly 90°.
Useful Conversion Table
| Term | Description | Example Value/Notes |
|---|---|---|
| Complementary Angle | Missing angle that complements the given angle | E.g., 40° if the given angle is 50° |
| Given Angle | Known angle | E.g., 30°, 45°, 60° |
| Total Sum of Angles | Total of complementary angles | Always equals 90° |
Example of Complementary Angle Calculator
Scenario 1: Given Angle = 40°
To find the complementary angle:
- Apply the Formula:
Complementary Angle = 90° – Given Angle
Complementary Angle = 90° – 40° - Result:
The complementary angle is 50°.
Scenario 2: Given Angle = 65°
To find the complementary angle:
- Apply the Formula:
Complementary Angle = 90° – Given Angle
Complementary Angle = 90° – 65° - Result:
The complementary angle is 25°.
Special Note:
If the given angle is greater than 90°, such as 100°, it does not have a complementary angle because the sum of two complementary angles cannot exceed 90°.
Most Common FAQs
Complementary angles are two angles whose measures add up to exactly 90 degrees. For example, if one angle is 60°, its complementary angle is 30° because 60° + 30° = 90°.
Simply input the known angle into the calculator, and it will subtract the given angle from 90° to display the complementary angle.
No, two right angles cannot be complementary because each right angle measures 90°, and the sum of two right angles would be 180°, which exceeds the definition of complementary angles.