Complementary Angle vs Supplementary Angle: Difference and Comparison

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.

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.

Key Takeaways

1. Complementary angles have a sum of 90 degrees, while supplementary angles add up to 180 degrees.
2. Complementary angles are used in right triangles, whereas supplementary angles frequently appear in linear pairs.
3. Two angles can be complementary or supplementary, but not simultaneously, as they represent different angle relationships.

Complementary Angle vs Supplementary Angle

A complementary angle is formed by two angles that complement each other. They form a right angle together that is the sum of their angles is 90 degrees. Supplementary angle is formed by two angles that supplement each other. They form a linear angle together that is the sum of their angles is 180 degrees.

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

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

1. When two complementary angles are added together, the sum is 90°, but when two supplementary angles are added together, the sum is 180°.
2. The sum of two complementary angles is π/2, but the sum of two supplementary angles is π.
3. 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°. 
4. If the two complementary angles are equal, they make 45 ° each, whereas if the two supplementary angles are equal, they make 90 ° each.
5. A complementary angle’s base makes a right angle, whereas a supplementary angle’s base makes a straight line. 

References

1. https://www.igi-global.com/chapter/how-gaming-and-formative-assessment-contribute-to-learning-supplementary-and-complementary-angles/294960
2. 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