1. What Are Complementary and Supplementary Angles?

Complementary angles are two angles whose measures add up to 90 degrees, while supplementary angles add up to 180 degrees. These relationships are fundamental in geometry and trigonometry.

2. How the Calculator Works

The calculator uses simple formulas to determine these angle relationships:

Where:

• θ — The input angle in degrees
• 90° — Right angle measure
• 180° — Straight angle measure

3. Practical Applications

Details: Understanding these angle relationships is essential in geometry proofs, architectural design, navigation, and various engineering applications where precise angle measurements are required.

4. Using the Calculator

Tips: Enter any angle between 0° and 360° to calculate its complementary and supplementary angles. Note that complementary angles only exist for angles ≤ 90°.

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is greater than 90°?
A: The complementary angle will be negative, indicating no actual complementary angle exists for angles >90°.

Q2: Can an angle be both complementary and supplementary?
A: No, unless the angle is 0°, which is trivial and not practically meaningful.

Q3: How precise are the calculations?
A: Results are calculated to 4 decimal places but displayed to 2 decimal places for readability.

Q4: Do these concepts apply to radians?
A: Yes, but you would use π/2 for complementary and π for supplementary angles instead of 90° and 180°.

Q5: What about angles greater than 360°?
A: The calculator normalizes angles between 0° and 360° by default.