1. What is the Complementary Angle Theorem?

The Complementary Angle Theorem states that two angles are complementary if their measures add up to 90 degrees. This calculator finds the complementary angle from a given angle θ.

2. How Does the Calculator Work?

The calculator uses the complementary angle formula:

Where:

• \( \theta \) — Given angle in degrees (must be between 0° and 90°)
• 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 an angle between 0 and 90 degrees. The calculator will return its complement (the angle that would make the sum equal to 90 degrees).

5. Frequently Asked Questions (FAQ)

Q1: What if I enter an angle greater than 90°?
A: The calculator will only accept angles between 0° and 90° as these are the only angles that have complements.

Q2: Can complementary angles be negative?
A: No, angle measures are always positive in standard geometry.

Q3: Are complementary angles always adjacent?
A: No, they don't need to be adjacent - they just need to sum to 90 degrees.

Q4: How is this different from supplementary angles?
A: Supplementary angles sum to 180°, while complementary angles sum to 90°.

Q5: Can three angles be complementary?
A: No, by definition only two angles can be complementary to each other.