1. What Are Supplementary Angles?

Two angles are supplementary when their measures add up to π radians (180 degrees). In radians, this relationship is expressed as θ + supp = π.

2. How Does the Calculator Work?

The calculator uses the supplementary angle formula:

Where:

• \( \theta \) — Given angle in radians
• \( \pi \) — Mathematical constant (~3.14159)
• \( \text{supp} \) — Supplementary angle in radians

Explanation: The formula simply subtracts the given angle from π radians to find its supplement.

3. Importance of Supplementary Angles

Details: Supplementary angles are fundamental in geometry, particularly in the study of parallel lines, polygons, and trigonometric identities. They help solve problems involving angle relationships in various geometric configurations.

4. Using the Calculator

Tips: Enter the angle in radians (0 ≤ θ ≤ π). The calculator will compute its supplementary angle. Remember that π radians equals 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between radians and degrees?
A: Radians and degrees are different units for measuring angles. π radians = 180 degrees. Radians are often preferred in higher mathematics.

Q2: Can an angle have more than one supplementary angle?
A: No, each angle has exactly one supplementary angle in the range (0, π).

Q3: What's the supplementary angle of 0 radians?
A: π radians (180 degrees) is supplementary to 0 radians.

Q4: Are supplementary angles always adjacent?
A: No, they don't need to be adjacent. They only need to add up to π radians.

Q5: How do I convert degrees to radians?
A: Multiply degrees by π/180. For example, 90° × π/180 = π/2 radians.