1. What Are Complementary and Supplementary Angles?

Complementary angles are two angles whose measures add up to 90 degrees. Supplementary angles are two angles whose measures add up to 180 degrees. These relationships are fundamental in geometry and trigonometry.

2. How the Calculator Works

The calculator uses simple formulas:

Where:

• \( \theta \) — The given angle in degrees

Note: An angle only has a complement if it's less than 90°. All angles less than 180° have supplements.

3. Practical Applications

Geometry: Used in solving problems with right angles (90°) and straight angles (180°).
Trigonometry: Complementary angles relate sine and cosine functions (sinθ = cos(90°-θ)).
Construction: Important for creating perpendicular and parallel structures.

4. Using the Calculator

Instructions: Enter any angle between 0° and 360°. The calculator will show its complement (if it exists) and supplement.

5. Frequently Asked Questions (FAQ)

Q1: Can an angle have both a complement and supplement?
A: Yes, if the angle is between 0° and 90° it will have both.

Q2: What's the supplement of a 90° angle?
A: 90° (since 180° - 90° = 90°).

Q3: Can complementary angles be negative?
A: No, angles are always positive in standard position.

Q4: What about angles greater than 180°?
A: The supplement will be negative, representing the reflex angle.

Q5: Are these relationships valid in radians?
A: Yes, but you'd use π/2 for 90° and π for 180°.