1. What is the Complementary Angle Theorem?

The Complementary Angle Theorem states that two angles are complementary if they add up to 90 degrees. This calculator finds the complementary angle for any given angle θ.

2. How Does the Calculator Work?

The calculator uses the complementary angle formula:

Where:

• \( θ \) — Given angle in degrees
• 90° — Right angle measure

Explanation: The calculator simply subtracts the input angle from 90 degrees to find its complement.

3. Importance of Complementary Angles

Details: Complementary angles are fundamental in geometry, especially in right triangle trigonometry and when working with perpendicular lines.

4. Using the Calculator

Tips: Enter the angle θ in degrees (must be between 0 and 90). The calculator will compute its complementary angle.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid input angles?
A: The input angle must be between 0° and 90° inclusive.

Q2: What if two angles are complementary?
A: Their measures add up to exactly 90 degrees.

Q3: Can complementary angles be negative?
A: No, angle measures are always positive in this context.

Q4: Are complementary angles always adjacent?
A: No, they don't need to be adjacent - they just need to sum to 90°.

Q5: What's the difference between complementary and supplementary angles?
A: Complementary angles sum to 90°, while supplementary angles sum to 180°.