What is Supplementary & Complementary Angle? Definition, Examples, Calculation


What is the Supplementary & Complementary angle? Any idea! In this article, we will learn all about Supplement & Complement angles along with definition, examples, calculation, etc. The sum of the measurements of two angles determines their complement and supplement. The pair of angles is complementary if the sum of their measurements equals a right angle. You must understand complement & supplement angles in order to have a thorough understanding of angles.

It can be said that complementary angles are two angles whose sum is 90 degrees, while supplementary angles are two angles whose sum is 180 degrees. It is not necessary for complementary and supplementary angles to be adjacent, share a vertex and a side, or be next to each other, but they can also be adjacent.

A vertex is a point at which two lines or segments meet. It is at this point that an angle is formed. An anti-clockwise rotation of a ray is measured by the angle formed between its initial and final positions when the ray rotates about its endpoint.

Definition of Complementary & Supplementary Angle

Definition of Complementary Angle

The definition of complementary angles in geometry is two angles with a sum of 90 degrees. An angle that adds up to 90 degrees is called a complementary angle. In this case, 50 degrees and 40 degrees are complement to each other.

For other example:

  • 60 degrees and 90-60 = 30 degrees are complement to each other.
  • 70 degrees and 90-70 = 20 degrees are complement to each other.
  • 75 degrees and 90-75 = 15 degrees are complement to each other.
  • 45 degrees and 90-45 = 45 degrees are complement to each other.
Complementary angle or complement angle
Complementary angle or complement angle

When two angles add up to 90 degrees, they are said to be complementary angles. When complementary angles are combined, they form a right angle or 90 degrees. If the sum of angles 1 and 2 equals 90 degrees, then angle 1 and angle 2 are complementary angles.

Definition Supplementary Angle

A straight line is formed by the addition of supplementary angles, which have a sum of 180 degrees. There are several angles that may be found by using supplementary angles.

supplementary angle or supplement angle
Supplementary angle or supplement angle

It is a congruent supplementary angle when the angle is tangent to the horizon, and when the angle is supplementary to the horizon. There are some unique angles that share these properties, and these angles should be learned when dealing with applications and problems that are related to angles and algebra, since these angles share these properties.

In this case, 120 degrees and 180 – 120 = 60 degrees are supplement to each other.

For other example:

  • 60 degrees and 180-60 = 120 degrees are supplement to each other.
  • 100 degrees and 180-100 = 80 degrees are supplement to each other.
  • 160 degrees and 180-160 = 20 degrees are supplement to each other.
  • 45 degrees and 180-45 = 135 degrees are supplement to each other.

Also Read: Volume of cylinder

Types of Complementary Angle

Complementary angles are those whose sum equals the measurement of a right angle. Complementary angles in geometry can be divided into two types:  

  • Adjacent Complementary Angle
  • Non-adjacent Complementary Angle

Adjacent Complementary Angle

The term adjacent complementary angles refers to two complementary angles which have a common vertex and a common arm. It shows that Angle COB and Angle AOB are adjacent angles because they have both a common vertex point ‘O’  and a common arm OB. The sum of the angles is 90 degrees.

COB + AOB = 70° + 20° = 90°. 

The two angles are complementary because they are adjacent to one another.  

Non-adjacent Complementary Angle

A non-adjacent complementary angle is a complementary angle that is not adjacent to another complementary angle.  There is neither a common vertex nor a common arm between Angle ABC and Angle PQR, making them non-adjacent angles. 

As well, Angle ABC and Angle PQR add up to 90 degrees, thus 50° + 40° = 90°. Consequently, these two angles are not adjacent but complementary. Complementary angles that are not adjacent form a right angle when they are joined together.

Also Read: Volume of sphere

Calculation of Complement & Supplement Angle

Calculating Complement of an Angle

In geometric terms, two complementary angles are equal to 90 degrees, and each is considered its complement. You can subtract 90 degrees from an angle to find its complement. 

The 90-x degree is the complement of the x degree. The next step is to find the complement of angle 57. By subtracting 57 degrees from 90 degrees, one gets 33 degrees, which is the complement of 57 degrees.  As a result, a 57-degree angle has a complement of 33 degrees.

Calculating Supplement of an Angle

An angle that adds up to 180 degrees is called a supplementary angle. Because the sum of 120 degree and 60 degree is 180 degree, angle 120 degree and angle 60 degree are supplementary angles. Subtract the given angle from 180 degrees in order to find the supplementary angle. A 60 degree angle would equal 180 minus 60 = 120 degrees.

Also Read: Perimeter of square

Properties of Complementary Angle & Supplementary Angle

Properties of Complementary Angle

  • When two angles add up to 90 degrees, they are said to be complementary.
  • There are two types of adjacent structures: adjacent and non-adjacent.
  • Even if the sum of three angles is 90 degrees, they cannot be complementary.
  • Complementary angles are called complement angles or complement angles of each other.
  • Right-angled triangles have complementary acute angles.

Properties of Supplementary Angle

  • A supplementary angle is one that adds up to 180° when two angles are added together.
  • It is not necessary for the two angles to be in the same plane to make a straight line.
  • The S of supplementary angles stands for the straight line, so that 180 degrees are formed.

Difference between Complementary & Supplementary Angle

Complementary refers to something that completes or complements another. An addition to something else is called a supplement. When two things are complementary, they have a stronger relationship whereas when they are supplementary, they are simply additional or auxiliary.

Complementary AngleSupplementary Angle
A 90-degree angle is equal to the sum of complementary angles.180 degrees are equal to the sum of supplementary degrees.
Each angle complements the other.Supplementing each other are two angles.
There is no linear pair of angles formed by these angles.A linear pair of angles is formed by these angles.
Designed only for right angles.Angles that are straight only should be used.
Difference between Complementary & Supplementary Angle

Also Read: Perimeter of a circle

Why Do You Need Complement & Supplement angle?

It is common to use the terms complementary and supplementary when describing the relationship between two angles that are complementary or supplementary. A complementary angle is defined as any angle whose measurements sum up to 90 degrees or, to put it another way, if two complementary angles are measured in the same way, their measurements will equal a right angle.

Whenever two angles are added together, their measurements will equal a total of 180 degrees or a straight line or straight angle if they are complementary angles. The complementary or supplementary relationship can be used if you know the measurement of one of these angles and you would like to find the measurement of the other angle using the complementary or supplementary relationship.

How to Remember Supplementary & Complementary Angle?

It is obvious that you may be confused these two angles many times, which may lead a wrong calculation and considerations. There is a simple way to remember supplement and complement angle! Let’s see

  • Supplement Angle: We have seen a straight line for supplement angle and total angle is 180 deg. Here, we need to remember, ‘S’ for Straight line which gives supplementary angle. In short, Supplement starts with ‘S’, which implies straight line.
  • Complement Angle: We have seen 90 deg angle in complementary angle. Here, we need to remember, ‘C’ for Canal which normally like 90 deg. In short, Complementary starts with ‘C’, which implies 90 deg.

Mathematical Problem of Supplementary & Complementary Angle

In this case, if one angle is two times the sum of the other angle and 6, find the both angles?

Let’s be assumed that A & B are the two angles which are complementary.

A + B = 90 (1)

According to the question, one angle is twice the sum of the other angle and 6.

Or, A = 2 (B+6)

Or, A = 2B + 12 (2)

Putting equation (2) value to equation (1)

Or, 2B + 12 +B = 90

Or, 3B +12 = 90

Or, 3B = 90 -12

Or, 3B = 78

Or, B = 78 / 3

Or, B = 26

Putting the value of B in Equation (1)

Or, A + 26 = 90

Or, A = 90 – 26

Or, A = 64

Answer:

A = 64 degree.

B = 36 degree.

Also Read: Place value & place value chart

There are two angles that are supplementary. Find the angles if one angle is 72 degrees less than twice the other angle?

Let’s be assumed that A & B are the two angles which are supplementary.

A + B = 180 (1)

The twice of the angle of one is 72 degrees less than the angle of the other.

Or, A = 2B – 72 (2)

Putting the value of A in Equation (1)

Or, 2B – 72 + B = 180

Or, 3B = 180 + 72

Or, B = 252 / 3

Or, B = 84

Putting the value of B in Equation (1)

Or, A + B = 180

Or, A + 84 = 180

Or, A = 180 – 84

Or, A = 96

Answer:

A = 96 degrees

B = 84 degrees.

It is important to note that the two angles have measures of (x + 35) degree and (3x + 25) degree respectively. If angle a and angle b are supplementary angles, then find the value of x. 

The sum of the supplementary angles is 180 degrees, as we know

Or, (x + 35) + (3x + 25) = 180

Or, 4x + 60 = 180

Or, 4x = 180 – 60

Or, 4x = 120

Or, x = 120 /4

Or, x = 30

Answer:  The value of x is 30 degree.

Approximately 80 degrees more than twice the measure of the complement of angle A makes up the supplement of angle A. How many degrees are there in the sum of the measures of angle A’s complement and supplement? 

Let p can be assumed to be the measure of angle A.

Complement of angle A = 90 – p

Supplement of angle A = 180 – p

There is an 80 degree difference between the measure of the supplement of angle A and the measure of the complement of angle A.

Or, 180 – p = 2 (90 – p) + 80

Or, 180 – p = 180 – 2p + 80

Or, 2p – p = 180 – 180 + 80

Or, p = 80

Complement of angle A = 90 – p

Or, A = 90 – 80

Or, A = 10

Supplement of angle A = 180 – p

Or, A = 180 – 80

Or, A = 100

The sum of supplement of complement of angle = 10 + 100 = 110 degree.

Answer:  The sum of supplement of complement of angle A = 110 degree.

There is a 50 degree difference between twice the complement of an angle and its supplement. Can you measure both angles?

Let p can be assumed to be the measure of angle A.

Complement of angle A = 90 – p

Supplement of angle A = 180 – p

It is 50 degrees less than its complement when an angle is twice its complement.

Or, 2 (90 – p) = (180 – p) – 50

Or, 180 – 2p = 180 – p – 50

Or, 2p – p = 180 – 180 – 50

Or, p = 50

Answer: As a result, 50 degrees is the measure of the angle. 

An angle’s supplement is also equal to thrice its measure. In degrees, what is the complement of an angle?

Let p can be assumed to be the measure of angle.

Supplement of the angle = 180 – p

An angle’s supplement equals thrice its measure.

Or, 180 – p = 3p

Or, 180 = 3p + p

Or, 180 = 4p

Or, 4p = 180

Or, p = 180 / 4

Or, p = 45

So the measure of the angle is 45 degree.

Therefore, the angle’s complement is = 90 – 45 = 45 degree.

Answer: It is 45 degrees to complement the angle. 

There is a supplementary angle between two angles. It is 3:7 if the smaller angle has a smaller measure than the larger angle. Can you tell me how big both angles are?

There are 3:7 ratios between the smaller angle and the larger angle.

Measure of the larger angle = 7S.

Measure of the smaller angle = 3S.

These two are supplementary to each other.

Or, 7S + 3S = 180

Or, 10 S = 180

Or, S = 180 /10

Or, S = 18

Measure of larger angle = 7S = 7 * 18 = 126 degree

Measure of smaller angle= 3S = 3* 18 = 54 degree

Answer: Larger Angle = 126 degree

Smaller Angle = 54 degree.

There is a complementary relationship between an angle and its fourth. Find the desired angle?

Let p can be assumed to be the measure of angle.

Therefore, one fourth of the angle is = p + p/4.

There is a complementary relationship between an angle and its one fourth. 

Or, p + p/4 = 90

Or, 4 (p+ p/4) = 4 * 90

Or, 4p + p = 360

Or, 5p = 360

Or, p = 360 / 5

Or, p = 72 degree

Answer: The measure of the angle is 72 degree.

Find the supplementary angle of 1/5 of 270 degree?

1/5 of 270 degree = 1/5 * 270 = 54 degree

Supplement angle of 54 degree = 180 – 54 = 126 degree.

Answer: The supplementary angle of 1/5 of 270 degree is 126 degree.

Find the two angles whose complementary ratio is twice the other angle so find the desired angle?

Let be assumed that p is one angle

Other angle = 2p

According to the question, both angles are complement to each other.

Or, p + 2p = 90

Or, 3p = 90

Or, p = 90 /3

Or, p = 30 degree

One angle = p= 30

Other angle = 2p = 2 * 30 = 60 degree

Answer: Both angles are 30 & 60 degree.

Approximately 4/3 of 30 degrees constitutes an angle. How do you measure the complementary angle? 

In this case, p is the measure of the complementary angle required.

4/3 of 30 degree of the measured angle

Or, 4/3 * 30 = 40 degree

We have 40 degree and p because they are complementary angles.

Or, P + 40 = 90

Or, P = 90 -40

Or, P = 50 

Answer: The complementary angle of measured angle is 50 degree.

In this supplementary case, you have to find the angle if 5 times of one angle is 15 times of the other angle?

Assume that a and b are supplementary angles.

Or, a + b = 180 (1)

An angle times five is equal to an angle times fifteen.

Or, 5a = 15b

Or, a = 3b (2)

Putting equation (2) value on equation (1) we get

Or, 3b + b = 180

Or, 4b = 180

Or, b = 180 / 4

Or, b = 45 degree

One angle = b = 45 degree

Other angle = a = 3b = 3 * 45 = 135 degree

Answer: Both the angles are 45 degree & 135 degree.

FAQs on Supplement & Complement angle

Can a supplementary angle become complementary angle?

A supplementary angle is not the same as a complementary angle. It can be observed that two angles form a pair of complementary angles when their sum is 90 degree, whereas two angles form a pair of supplementary angles when their sum is 180 degree.

How can you measure if an angle is supplementary or complementary?

When the measures of two angles add up to 90 degrees, they are called complementary angles. 
Supplementary angles are those whose measures add up to 180 degrees. Note that in the alphabet, s comes after c, and 180 are greater than 90 to avoid mixing up these definitions.

Can a vertical angle be supplementary or complementary?

There are two types of vertical angles: supplementary angles and complementary angles. Whenever there is an intersection of two lines that creates an angle directly across from each other, these angles are called vertical angles. It is said that supplementary angles are those where the sum of the two angles exceeds 180 degrees.

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