Find The Measure Of Complementary And Supplementary Angles Calculator

Enter an angle to find its complementary and supplementary angles instantly with our easy-to-use complementary and supplementary angles calculator.

Angle Calculator

What is a Complementary and Supplementary Angles Calculator?

A complementary and supplementary angles calculator is a tool used to determine the measures of the complementary and supplementary angles for a given angle. Complementary angles are two angles that add up to 90 degrees, while supplementary angles are two angles that add up to 180 degrees. This calculator is useful for students, teachers, engineers, and anyone working with geometric figures or angle measurements. It simplifies the process of finding these related angles without manual calculation.

Many people use a complementary and supplementary angles calculator to quickly check their geometry homework or to find the missing angle in a pair of complementary or supplementary angles. Common misconceptions are that any two angles can be complementary or supplementary, but they must add up to exactly 90 or 180 degrees, respectively, and are usually considered as positive angle measures.

Complementary and Supplementary Angles Formula and Mathematical Explanation

The formulas used by the complementary and supplementary angles calculator are straightforward:

• Complementary Angle: If you have an angle 'A', its complement 'C' is found by the formula: C = 90° – A. This is only valid if 0° ≤ A ≤ 90°.
• Supplementary Angle: If you have an angle 'A', its supplement 'S' is found by the formula: S = 180° – A. This is valid if 0° ≤ A ≤ 180°.

Let's say you have an angle A. If A and another angle C are complementary, then A + C = 90°. Therefore, C = 90° – A. If A and another angle S are supplementary, then A + S = 180°. Therefore, S = 180° – A.

The complementary and supplementary angles calculator applies these formulas based on the input angle.

Variables Used

Variables in the complementary and supplementary angle calculations.

Variable	Meaning	Unit	Typical Range
A	Input Angle	Degrees (°)	0 – 180
C	Complementary Angle	Degrees (°)	0 – 90 (or N/A)
S	Supplementary Angle	Degrees (°)	0 – 180

Practical Examples (Real-World Use Cases)

Let's see how the complementary and supplementary angles calculator works with some examples.

Example 1: Angle of 35°

• Input Angle (A): 35°
• Complementary Angle (C): 90° – 35° = 55°
• Supplementary Angle (S): 180° – 35° = 145°
• The angle 35° is acute.

Example 2: Angle of 110°

• Input Angle (A): 110°
• Complementary Angle (C): Not applicable (since 110° > 90°)
• Supplementary Angle (S): 180° – 110° = 70°
• The angle 110° is obtuse.

The complementary and supplementary angles calculator would provide these results instantly.

How to Use This Complementary and Supplementary Angles Calculator

1. Enter the Angle: Type the measure of the angle (between 0 and 180 degrees) into the "Enter Angle (in degrees)" input field.
2. View Results: The calculator automatically updates and displays the complementary angle (if applicable), the supplementary angle, and the type of the input angle (acute, right, obtuse, or straight). The visual chart also updates.
3. Reset: Click the "Reset" button to clear the input and results and set the angle to the default value (30°).
4. Copy Results: Click "Copy Results" to copy the input angle, complementary angle, supplementary angle, and angle type to your clipboard.

Using the complementary and supplementary angles calculator helps you understand the relationship between angles quickly.

Key Factors That Affect Complementary and Supplementary Angles Results

The primary factor affecting the results from the complementary and supplementary angles calculator is the value of the input angle itself.

• Input Angle Value: The magnitude of the angle you enter directly determines the values of its complement and supplement.
• Angle Range (0-90°): If the angle is between 0° and 90°, it will have both a complementary and a supplementary angle.
• Angle Value (90°): A right angle (90°) has a complement of 0° and a supplement of 90°.
• Angle Range (90-180°): If the angle is between 90° and 180°, it will not have a positive complementary angle in the traditional sense, but it will have a supplementary angle.
• Angle Value (180°): A straight angle (180°) has no positive complement and a supplement of 0°.
• Understanding Definitions: Misunderstanding the definitions of complementary (add to 90°) and supplementary (add to 180°) will lead to incorrect manual calculations, which the complementary and supplementary angles calculator avoids.

Frequently Asked Questions (FAQ)

What are complementary angles?

Complementary angles are two angles that add up to 90 degrees. Our complementary and supplementary angles calculator finds the complement for angles between 0° and 90°.

What are supplementary angles?

Supplementary angles are two angles that add up to 180 degrees. The complementary and supplementary angles calculator finds the supplement for angles between 0° and 180°.

Can an angle have both a complement and a supplement?

Yes, if an angle is between 0° and 90° (exclusive of 0 if we consider positive angles), it will have both a positive complementary and a positive supplementary angle.

What is the complement of 90 degrees?

The complement of 90 degrees is 0 degrees.

What is the supplement of 90 degrees?

The supplement of 90 degrees is 90 degrees.

What is the complement of an angle greater than 90 degrees?

In the usual sense (dealing with positive angles adding up to 90), an angle greater than 90 degrees does not have a positive complement. The complementary and supplementary angles calculator indicates this.

Do complementary or supplementary angles need to be adjacent?

No, they do not need to be adjacent. They just need to add up to 90° or 180°, respectively.

Why does the calculator limit input to 180 degrees?

While angles can be larger, the concepts of complementary and supplementary angles are most commonly applied and defined within the 0° to 180° range for simple geometric figures and angle pairs. The complementary and supplementary angles calculator focuses on this common range.