1. What is a Supplementary Angle?

Two angles are supplementary when their measures add up to 180 degrees. This concept is fundamental in geometry, particularly when working with linear pairs of angles or parallel lines cut by a transversal.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( \theta \) — The given angle in degrees (must be between 0° and 180°)
• \( \text{supp} \) — The supplementary angle result in degrees

3. Practical Applications

Geometry: Supplementary angles are essential when proving geometric theorems, analyzing polygon angles, and solving problems involving parallel lines.

Construction: Used in architectural design and engineering to ensure proper angles in structural components.

4. Using the Calculator

Instructions: Enter any angle between 0 and 180 degrees. The calculator will instantly compute its supplementary angle (180° - θ).

Note: Angles must be in degrees (not radians) and within the valid range of 0° to 180°.

5. Frequently Asked Questions (FAQ)

Q1: Can an angle be supplementary to itself?
A: Only if the angle is exactly 90°, since 90° + 90° = 180°.

Q2: What's the difference between complementary and supplementary angles?
A: Complementary angles sum to 90°, while supplementary angles sum to 180°.

Q3: Do supplementary angles have to be adjacent?
A: No, they only need to sum to 180°. Adjacent supplementary angles form a linear pair.

Q4: What's the supplementary angle of 0°?
A: 180°, since 0° + 180° = 180°.

Q5: Can three angles be supplementary?
A: Yes, if their measures sum to 180°, though typically we refer to pairs of angles as supplementary.