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. When one angle is known, its complement can be found by subtracting it from 90°.

2. How Does the Calculator Work?

The calculator uses the complementary angle formula:

Where:

• \( \theta \) — Known angle in degrees (must be between 0° and 90°)
• Complementary — Angle that completes θ to 90°

Explanation: The formula calculates the angle that when added to θ results in a right angle (90°).

3. Importance of Complementary Angles

Details: Complementary angles are fundamental in geometry, especially in right triangles where the two non-right angles are always complementary. They're also important in trigonometry and various engineering applications.

4. Using the Calculator

Tips: Enter the known angle θ in degrees (must be between 0 and 90). The calculator will compute its complement (the angle that adds up to 90° with θ).

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is greater than 90°?
A: Angles greater than 90° cannot have complements in standard geometry as their complements would be negative. The calculator only accepts angles between 0° and 90°.

Q2: Can complementary angles be negative?
A: No, in standard geometry, angle measures are always positive. The complement must be between 0° and 90°.

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

Q4: What's the difference between complementary and supplementary angles?
A: Complementary angles sum to 90°, while supplementary angles sum to 180°.

Q5: How are complementary angles used in real life?
A: They're used in construction (determining roof angles), navigation, and various engineering applications where right angles are involved.