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 of a given angle θ.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( \theta \) — The given angle in degrees
• 90° — Right angle measure

Explanation: The formula directly calculates the angle that would complete the given angle to form a right angle (90°).

3. Importance of Complementary Angles

Details: Complementary angles are fundamental in geometry, especially in right triangle trigonometry and when working with perpendicular lines. They help in solving various geometric problems and proofs.

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 if my angle is greater than 90°?
A: Angles greater than 90° don't have complementary angles (since their sum with any positive angle would exceed 90°).

Q2: Can complementary angles be negative?
A: No, both angles in a complementary pair must be positive and their sum must be exactly 90°.

Q3: Are complementary angles always adjacent?
A: No, they don't have to be adjacent. They just need to add up to 90°.

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

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