## Complementary and Supplementary Angles Definition

Complementary and supplementary angles are the two types of angles based on their measures. An angle that measures 900 is a complementary angle and whose measure is 1800 is a supplementary angle.

We have studied basic geometrical terms. We know that two lines having a common vertex form an angle. Various parts of an angle are vertex, arms, interior, and exterior of angles. When two lines intersect they form four angles at the point of intersection. An angle is denoted by the symbol ∠.

From the figure, ∠ABC is an angle. B is the point of intersection called the vertex and AB and BC are the sides of the angle. Angles are commonly measured in terms of degree.

Angles are Classified According to Their Sizes as Follows

• Acute angle
• Obtuse angle
• Right angle
• Reflex angle

There are more types of angles on the basis of the pairs of angles. They are as follows

• Complementary angles
• Supplementary angles
• Vertically opposite angles
• Linear Pairs

In this session, we will be learning complementary and supplementary angles in detail.

### Complementary Angles Definition

When the sum of the measure of two angles is 900, then the pair of angles is said to be complementary angles. In complementary angles one angle is a complement of the other making a sum of 900  or you can say forming a right angle.

From the figure, we can say that ∠ABC + ∠CBD = 50 + 40 = 900. This is an example of complementary angles example

But it is not necessary that the two complementary angles are always adjacent to each other. They can be different angles, only their sum should be 900

Figure given below is a complementary angle example 27 + 63 = 900.

### Supplementary Angles Definition

When the sum of the measure of two angles is 1800, then the pair of angles is said to be supplementary angles. Here the supplementary meaning is one angle is supplemented to another angle to make a sum of 1800.

Supplementary angles example

From the figure, we can say that  ∠1 +  ∠2 = 1800

But it is not necessary that the two supplementary angles are always adjacent to each other. They can be different angles, only their sum should be 1800

From the figure, ∠3  and  ∠4 are not adjacent but they make a supplementary angle if their sum is 1800.

Supplementary angles example

### Properties of Supplementary Angles

• According to supplementary angles definition two angles are said to be a supplementary angle if the sum of their measures is 1800.
• It is not necessary that a supplementary angle will lie on the same line, they can be on different lines but should measure 1800.
• In the supplementary angles if one is an acute angle then the other is an obtuse angle.
• In a supplementary angle if one angle is 900 the other angle will also be 900.

### Properties of Complementary Angles

• According to supplementary angles definition two angles are said to be a complementary angle if the sum of their measures is 900.
• It is not necessary that a supplementary angle will lie on the same line, they can be on different lines but should measure 900.

How to Find Two Angles are Complementary?

If measures of two angles are given. Add them. If the sum of the measures of these two angles is 900, then the two angles are complementary angles.

If the two angles are given as complementary angles and if the measure of one angle is given we can find the other angle.

For example : ∠A + ∠B = 90° and ∠A = 300 , then ∠B = ?

∠B = 90 – ∠A

∠B = 90 – 30

∠B = 60

The formula for finding a complementary angle is 90 – x, where x is the measure of one of the angles.

How to Find Two Angles are Supplementary?

If measures of two angles are given. Add them. If the sum of the measures of these two angles is 1800, then the two angles are supplementary angles.

If the two angles are given as supplementary angles and if the measure of one angle is given we can find the other angle.

For example : ∠A + ∠B = 180° and ∠A = 800 , then ∠B = ?

∠B = 180 – ∠A

∠B = 180 – 80

∠B = 1000

The formula for finding a supplementary angle is 180 – x, where x is the measure of one of the angles.

### Fun Facts

• In a right-angled triangle, the two non-right angles are complementary angles to each other.
• Complementary comes from the Latin word ‘completum’ meaning “completed” because the right angle is thought of as being a complete angle.
• Supplement comes from Latin word ‘supplere’, to complete or “supply” what is needed.

### Solved Examples

Example 1: Two angles are supplementary. One of these two angles is 1100 and finds the other angle.

Solution: One angle is given 1100

Let the other angle be x

Given that the two angles are supplementary we have,

The sum of the measures of these two angles is 1800

x + 110 = 1800

x = 180 – 110

x = 700

So the other angle is 700

Example 2: The measure of an angle is 72°. What is the measure of a complementary angle?

Solution: Let x be the measure of the complementary angle.

Because x and 62° are complementary angles, we have

x + 62°  =  90°

x = 90 – 72

x = 18

So, the measure of the complementary angle is 18°.

Example 3: Find the Supplement of the angle 1/3 of 240°.

Solution:

Convert 1/3 of 240°

That is, 1/3 x 240° = 80°

The sum of the measures of these two angles is 1800

x + 80 = 1800

x = 180 – 80

x = 1000

Therefore, Supplement of the angle 1/3 of 240° is 100°

### Quiz Time

Supplementary Angles Examples

1. The measure of an angle is 100°. What is the measure of a supplementary angle?

2. .Find the value of x

Complementary Angles Examples

1. The measure of an angle is 22°. What is the measure of a complementary angle?

2. Find the value of x

What is the difference between Complementary and Supplementary angles?

Here are some differences between difference between Complementary

and Supplementary angles

• According to supplementary angle definition If the sum of the measure of two angles is 1800 then the angles are said to be supplementary angles, whereas according to complementary angles definition if the sum of measures of two angles is 900 then the angles are called complementary angles.

•  Supplementary angles together form a straight line whereas complementary angles together form a right angle.

• Two angles ∠A and ∠B  are supplementary angles if ∠A + ∠B = 1800, while two angles ∠A and ∠B are complementary if ∠A + ∠B = 900

• Example of supplementary angle

∠1 + ∠2 = 1800

Example of Complementary angle

∠1 + ∠2 = 900

What is another name for supplementary angles?

Another name for supplementary angle is straight angle. Because according to supplementary angle definition two angles are supplementary if their sum adds up to 1800. Similarly the straight angle measures 1800. They both make a complete half turn.

What is zero angle?

As the name implies, an angle that measures 0o  is called a zero angle. You can assume two sides of an angle overlaps each other.