1. What is a Complementary Angle?

Two angles are complementary when the sum of their measures is exactly 90 degrees. In geometry, complementary angles form a right angle when placed adjacent to each other.

2. How Does the Calculator Work?

The calculator uses the complementary angle formula:

Where:

• \( \theta \) — Given angle in degrees
• \( 90^\circ \) — Right angle measure

Explanation: The formula subtracts the given angle from 90 degrees to find its complement.

3. Importance of Complementary Angles

Details: Complementary angles are fundamental in geometry, trigonometry, and various practical applications like construction, engineering, and design where right angles are essential.

4. Using the Calculator

Tips: Enter an angle between 0 and 90 degrees. The calculator will compute its complementary angle (the angle that when added to your input equals 90 degrees).

5. Frequently Asked Questions (FAQ)

Q1: Can an angle have more than one complementary angle?
A: No, each acute angle (less than 90°) has exactly one complementary angle that makes the sum equal to 90°.

Q2: What if I enter an angle greater than 90 degrees?
A: The calculator only accepts angles between 0-90 degrees as angles greater than 90° cannot have complementary angles in standard geometry.

Q3: Are complementary angles always adjacent?
A: No, complementary angles don't need to be adjacent. They only need to sum to 90 degrees regardless of their position.

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

Q5: Can two obtuse angles be complementary?
A: No, since obtuse angles are greater than 90°, two such angles would sum to more than 180°, making it impossible for them to be complementary.