1. What Are Complementary and Supplementary Angles?

Complementary angles are two angles that add up to 90 degrees, while supplementary angles add up to 180 degrees. These relationships are fundamental in geometry, especially when working with right triangles and straight lines.

2. How the Calculator Works

The calculator uses these simple formulas:

Where:

• \( θ \) — The given angle in degrees
• 90° — Right angle measure
• 180° — Straight angle measure

3. Applications in Geometry

Details: Understanding these angle relationships is essential for solving problems involving triangles, parallel lines cut by a transversal, and polygon interior angles.

4. Using the Calculator

Tips: Enter any angle between 0° and 360°. The calculator will show its complementary angle (if θ ≤ 90°) and supplementary angle (if θ ≤ 180°).

5. Frequently Asked Questions (FAQ)

Q1: Can an angle have both complementary and supplementary angles?
A: Yes, angles between 0° and 90° have both complementary and supplementary angles.

Q2: What if my angle is greater than 90°?
A: Angles >90° don't have complementary angles but may have supplementary angles if ≤180°.

Q3: How are these concepts used in triangles?
A: In right triangles, the non-right angles are complementary. Supplementary angles help solve for unknown angles in various geometric figures.

Q4: What about negative angles or angles >360°?
A: The calculator works with angles 0°-360°. For angles outside this range, use modulo 360 to find equivalent angle within range.

Q5: Are there complementary/supplementary relationships in radians?
A: Yes, complementary would be π/2 - θ and supplementary would be π - θ.