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Last updated on August 5th, 2025

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Supplementary Angles Formula

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In geometry, supplementary angles are two angles whose measures add up to 180 degrees. These angles can be adjacent or non-adjacent. In this topic, we will learn the formula for calculating supplementary angles.

Supplementary Angles Formula for UAE Students
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List of Formulas for Supplementary Angles

Supplementary angles add up to 180 degrees.

 

Let’s learn the formula to determine supplementary angles.

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Supplementary Angles Formula

The formula for supplementary angles is simple and straightforward.

 

If two angles are supplementary, the sum of their measures is 180 degrees.

 

This is expressed as: Angle A + Angle B = 180°

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Calculating One Angle Given the Other

If one angle measure is known, the other angle can be found using the formula:

 

Angle B = 180° - Angle A

 

This formula is used when you know one of the supplementary angles and need to find the other.

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Examples of Supplementary Angles

Let's look at some examples to understand how to use the supplementary angles formula:

 

If one angle is 70°, the supplementary angle is: 180° - 70° = 110°

 

Thus, the supplementary angle is 110°.

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Importance of Supplementary Angles Formula

In geometry and real-life applications, the supplementary angles formula helps solve various problems involving linear pairs and angle measurements.

 

Here are some reasons why understanding this concept is important:

 

- It aids in solving geometric proofs and problems.

- It is essential in architectural and engineering designs involving linear structures.

- Understanding supplementary angles helps in the study of parallel lines and transversal angles.

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Tips and Tricks to Memorize Supplementary Angles Formula

Students might find remembering angle formulas tricky, but here are some tips and tricks to master them:

 

- Remember that supplementary means "adds up to 180°."

- Visualize a straight line, which is 180°, and think of how two angles can fit on that line.

- Use flashcards to memorize the formula and practice with different angle measurements.

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Common Mistakes and How to Avoid Them While Using Supplementary Angles Formula

Students make errors when dealing with supplementary angles.

Here are some mistakes and ways to avoid them:

Mistake 1

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Forgetting the Total Must Be 180°

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Students sometimes forget that supplementary angles must add up to 180°. To avoid this error, always double-check your calculations to ensure the total is 180°.

Mistake 2

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Confusing Complementary with Supplementary

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Students often confuse complementary angles (which sum to 90°) with supplementary angles. Remember, supplementary angles sum to 180°.

Mistake 3

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Incorrectly Calculating the Unknown Angle

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Errors occur when calculating the unknown angle from a known angle. Always use the formula: Angle B = 180° - Angle A to find the correct measure.

Mistake 4

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Ignoring Units

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Sometimes students forget to specify units (degrees). Ensure all angle measures are in degrees when using the supplementary angles formula.

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Examples of Problems Using Supplementary Angles Formula

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Problem 1

If one angle measures 45°, what is the supplementary angle?

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The supplementary angle is 135°

Explanation

To find the supplementary angle, subtract the known angle from 180°: 180° - 45° = 135°

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Problem 2

Find the supplementary angle of 120°.

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The supplementary angle is 60°

Explanation

To find the supplementary angle, subtract the known angle from 180°: 180° - 120° = 60°

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Problem 3

Two angles are supplementary. If one angle is 85°, what is the other angle?

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The other angle is 95°

Explanation

To find the other angle, subtract the known angle from 180°: 180° - 85° = 95°

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FAQs on Supplementary Angles Formula

1.What is the formula for supplementary angles?

The formula for supplementary angles is: Angle A + Angle B = 180°

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2.How do you find one supplementary angle if you know the other?

To find one supplementary angle, subtract the known angle from 180°.

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3.Can supplementary angles be adjacent?

Yes, supplementary angles can be adjacent and form a linear pair, or they can be non-adjacent.

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4.Are all linear pairs of angles supplementary?

Yes, all linear pairs of angles are supplementary because they form a straight line.

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5.What is a real-life example of using supplementary angles?

In architecture, supplementary angles are used to ensure that structures meet at the correct angles to maintain stability.

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Glossary for Supplementary Angles Formula

  • Supplementary Angles: Two angles that add up to 180 degrees.

     
  • Linear Pair: A pair of adjacent angles that form a straight line, adding up to 180 degrees.

     
  • Adjacent Angles: Angles that share a common side and vertex.

     
  • Complementary Angles: Two angles whose measures add up to 90 degrees.

     
  • Angle Measure: The degree of an angle, often measured in degrees.
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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