Two half-lines, also known as rays, which meet at a common point create a space between them. An angle can be used to measure this space near the endpoint.

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Angles are described as having arms and legs, while their vertex is described as being the endpoint. Radian measurements and degrees are both used to describe angles.

Angles are an important concept that can be used in many different ways in both mathematics and physics. Supplementary and complementary angles are two widely used terms.

Having a deep understanding of what these terms mean can help an individual solve so many problems.

**Complementary Angle vs Supplementary Angle**

**The main difference between a complementary angle and a supplementary angle is that the two angles that make up a complementary angle have a sum of 90°, whereas the two angles that make up a supplementary angle have a sum of 180°. **

Complementary angles are formed when the sum of a pair of angles is exactly 90°. A right angle is formed when two complementary angles are adjacent to each other.

For example, two angles measuring 65 ° and 25 ° respectively can be considered complementary as their sum is exactly 90 °.

Whenever the sum of two angles is exactly 180°, they are called supplementary angles. Straight angles are formed by joining supplementary angles together.

For example, if two angles measure 110° and 70° respectively, they can be regarded as supplementary angles because their sum equals 180°.

**Comparison Table Between Complementary Angle and Supplementary Angle**

Parameters of Comparison | Complementary Angle | Supplementary Angle |

Sum of the angles in degrees | The sum of the two included angles is 90°. | The sum of the two included angles is 180°. |

Sum of the angles in π | The sum of the two included angles is π/2. | The sum of the two included angles is π. |

Description of the angles | Both the angles involved are acute, i.e., they are less than 90°. | One angle is acute and the other is obtuse, i.e., one is less than 90° and the other is more than 90°. |

Equal angles | If the two complementary angles are equal, they are 45 ° each. | If the two supplementary angles are equal, they are 90 ° each. |

The base of the angles | The base of complementary angles makes a right angle. | The base of supplementary angles makes a straight line. |

**What is a Complementary Angle?**

When the sum of two angles is 90°, the angles are called complementary angles. If any pair of angles sum comes out to be even a degree off than 90°, say 89° or 90°, then they cannot be determined as complementary angles.

The sum of two complementary angles needs to be exactly 90°. In terms of π, the sum of two complementary angles needs to be π/2.

So, for instance, ∠ACD = 70° and ∠BCD = 20° can be called a pair of complementary angles as their sum (70° + 20°) comes out to be exactly 90°.

Angles less than 90° are known as acute angles. Since angles cannot be negative, both the angles included in a complementary angle are acute.

If a complementary angle is broken into two equal parts, we get two angles of 45° each. Thus two complementary angles can be equal only if they both measure 45 °.

If two complementary angles are placed adjacent to each other, the base of both the angles would make a right angle.

**What is a Supplementary Angle?**

When the sum of two angles is 180°, the angles are called supplementary angles. If any pair of angles sum comes out to be even a degree off than 180°, say 179° or 181°, then they cannot be determined as supplementary angles.

The sum of two supplementary angles needs to be exactly 180°. In terms of π, the sum of two supplementary angles needs to be π.

So, for instance, ∠ACD = 120° and ∠BCD = 60° can be called a pair of supplementary angles as their sum (120° + 60°) comes out to be exactly 180°.

Angles less than 180 ° but more than 90 ° are known as obtuse angles. Thus out of the two angles involved, one of the angles needs to be acute, while the other needs to be obtuse.

That is, one of them must be less than 90° while the other must be more than 90°. If a supplementary angle is broken into two equal parts, we get two angles of 90° each.

Thus two supplementary angles can be equal only if they both measure 90°. If two supplementary angles are placed adjacent to each other, the base of both the angles would be a straight line.

**Main Differences Between Complementary Angle and Supplementary Angle**

- When two complementary angles are added together, the sum is 90°, but when two supplementary angles are added together, the sum is 180°.
- The sum of two complementary angles is π/2, but the sum of two supplementary angles is π.
- Complementary angles are both acute angles, i.e., they are both less than 90°, while supplementary angles have one acute and one obtuse angle, i.e., one is less than 90° and the other is more than 90°.
- If the two complementary angles are equal, they make 45 ° each, whereas if the two supplementary angles are equal, they make 90 ° each.
- A complementary angle’s base makes a right angle, whereas a supplementary angle’s base makes a straight line.

**Conclusion**

The terms complementary and supplementary angles are related, but they are not the same. The angles that form a complementary angle and a supplementary angle are different, so they serve different purposes.

People often have trouble remembering the sum of complementary and supplementary angles. Various methods can be used to address this issue.

Two, in particular, are very well known. The first follows that since complementary angles always start with a “C”, which comes before the “S”, complementary angles must have a smaller sum, i.e. 90° and not 180°.

Another states that complementary begins with a “C”, as does the word “corner,” which is what an adjacent complementary angle looks like. Additionally, the word supplementary begins with “S” as does the word “straight”, which is what an adjacent supplementary angle looks like.

The two concepts are equally important in science and mathematics.

**References**

- https://www.igi-global.com/chapter/how-gaming-and-formative-assessment-contribute-to-learning-supplementary-and-complementary-angles/294960
- https://www.researchgate.net/profile/Leonor-Santos/publication/357205282_How_Gaming_and_Formative_Assessment_Contribute_to_Learning_Supplementary_and_Complementary_Angles/links/61c1a980c99c4b37eb1191c7/How-Gaming-and-Formative-Assessment-Contribute-to-Learning-Supplementary-and-Complementary-Angles.pdf