Complementary and Supplementary Angles Calculator

Angle Relationships:

\[ \text{Complementary} = 90° - \theta \] \[ \text{Supplementary} = 180° - \theta \]

Complementary Angle:

Supplementary Angle:

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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 and trigonometry.

2. How the Calculator Works

The calculator uses simple formulas:

\[ \text{Complementary Angle} = 90° - \theta \] \[ \text{Supplementary Angle} = 180° - \theta \]

Where:

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

3. Practical Applications

Details: These angle relationships are used in construction, engineering, navigation, and various fields of mathematics including trigonometry and geometry.

4. Using the Calculator

Tips: Enter any angle between 0° and 360°. The calculator will show the complementary angle (if it exists) and supplementary angle (if it exists).

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 angles have no complements?
A: Angles 90° or greater have no complementary angles.

Q3: What angles have no supplements?
A: Angles 180° or greater have no supplementary angles.

Q4: Are the results always positive?
A: The calculator only shows positive results. Negative results mean no such angle exists.

Q5: Can I use decimal values?
A: Yes, the calculator accepts decimal values for more precise calculations.