# Supplementary And Complementary Angles

**Supplementary angles and complementary angles** are defined with regard to the addition of two angles. If the union of two angles is 180 degrees then they are said to be supplementary angles, which forms a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary color angles, and they form a justly angle in concert .

When two line segments or lines meet at a common point ( called vertex ), at the point of intersection an angle is formed. When a ray is rotated about its end point, then the measure of its rotation in an anti-clockwise direction is the angle formed between its initial and final position .

In libyan islamic fighting group. 1 if the beam \ ( \small \overrightarrow { OP } \ ) is rotated in the management of the ray \ ( \small \overrightarrow { OQ } \ ), then the measure of its rotation represents the slant formed by it. In this case, the measure of rotation that is the angle formed between the initial side and the terminal side is represented by Ɵ .

## complementary color Angles

When the union of two angles is 90°, then the angles are known as **complementary angles**. In other words, if two angles add up to form a right fish, then these angles are referred to as complementary angles. hera we say that the two angles complement each other .

presuppose if one angle is x then the early lean will be 90o – x. Hence, we use these complementary angles for trigonometry ratios, where on ratio complement another proportion by 90 degrees such as ;

- sin (90°- A) = cos A and cos (90°- A) = sin A
- tan (90°- A) = cot A and cot (90°- A) = tan A
- sec (90°- A) = cosec A and cosec (90°- A) = sec A

Hence, you can see here the trigonometric ratio of the angles gets changed if they complement each other .

In the above figure, the measuring stick of angle BOD is 60o and fish AOD measures 30o. On adding both of these angles we get a right angle, therefore ∠BOD and ∠AOD are complementary color angles .

The follow angles in Fig. 3 given below are complementary color to each early as the measure of the sum of both the angles is 90o. ∠POQ and ∠ABC are complemental and are called **complements** of each other .

** For example:** To find the complement of 2x + 52°, subtract the given slant from 90 degrees .

90o – ( 2x + 52o ) = 90o – 2x – 52o = -2x + 38o

The complement of 2x + 52o is 38o – 2x .

**Facts of complementary angles:**

- Two right angles can not complement each early
- Two obtuse angles can not complement each other
- Two complemental angles are acute accent but frailty versa is not possible

## Supplementary Angles

When the kernel of two angles is 180°, then the angles are known as auxiliary angles. In other words, if two angles add up, to form a square angle, then those angles are referred to as **supplementary angles** .

The two angles form a linear slant, such that, if one angle is x, then the other the angle is 180 – ten. The one-dimensionality here proves that the properties of the angles remain the same. Take the examples of trigonometric ratios such as ;

- Sin (180 – A) = Sin A
- Cos (180 – A) = – Cos A (quadrant is changed)
- Tan (180 – A) = – Tan A

In Fig. 4 given above, the bill of ∠AOC is 60o and ∠AOB measures 120o. On adding both of these angles we get a true angle. consequently, ∠AOC and ∠AOB are supplementary angles, and both of these angles are known as a accessory of each early .

**Also, learn:**

### dispute between Complementary and Supplementary Angles

**Complementary Angles**

**Supplementary Angles**

Sum is equal to 90 degrees

Sum is adequate to 180 degrees

Two angles complement each other

Two angles supplement each other

It is not defined for linear match of angles

It is defined for linear pair of angles

Meant only for right angles

Meant only for square angles

How to remember easily the difference between Complementary angle and supplementary angles ?

- “
**C**“**letter of****C**omplementary stands for “**C**orner” (A right angle, 90o) - “
**S**“**S**upplementary stands for “**S**traight” ( a straight line, 180o)

## Solved Examples

The example problems on auxiliary and complementary color angles are given below :

**Example 1:**

Find the complement of 40 degrees .

**Solution:**

As the given angle is 40 degrees, then ,

complement is 50 degrees .

We know that Sum of Complementary angles = 90 degrees

so, 40° + 50° = 90°

**Example 2:**

Find the Supplement of the fish 1/3 of 210°.

**Solution: **

**Step 1:** Convert 1/3 of 210°

That is, 1/3 ten 210° = 70°

**Step 2: ** Supplement of 70° = 180° – 70° = 110°

therefore, Supplement of the slant 1/3 of 210° is 110°

**Example 3:**

The measures of two angles are ( x + 25 ) ° and ( 3x + 15 ) °. Find the value of adam if angles are supplementary angles .

**Solution: **

We know that, **Sum of Supplementary angles = 180 degrees**

so ,

( ten + 25 ) ° + ( 3x + 15 ) ° = 180°

4x + 40° = 180°

4x = 140°

ten = 35°

The respect of x is 35 degrees .

**Example 4:**

The deviation between two complementary color angles is 52°. Find both the angles .

**Solution: **

Let, First angle = thousand degrees, then ,

second slant = ( 90 – thousand ) degrees { as per the definition of complementary angles }

difference between angles = 52°

now ,

( 90° – thousand ) – thousand = 52°

90° – 2m = 52°

– 2m = 52° – 90°

-2m = -38°

megabyte = 38°/2°

megabyte = 19°

again, Second angle = 90° – 19° = 71°

consequently, the want angles are 19°, 71° .

### Practice Questions

- Check if 65° and 35° are complementary angles .
- Is 80° and 100° supplementary ?
- Find the complement of 54° .
- Find the supplement of 99° .
- If one lean measures 50° and is supplementary to another fish. then find the value of another slant. besides, express what type of angle it is ?

## frequently Asked Questions – FAQs

### What are complementary angles? Give example.

When the union of two angles is peer to 90 degrees, they are called complementary color angles. For example, 30 degrees and 60 degrees are complementary angles .

### What are supplementary angles? Give examples.

When the sum of the measure of two angles is equal to 180 degrees, they are called auxiliary angles. For case, 70 degrees and 110 degrees are auxiliary .

### How to find complementary angles?

Since, the summarize of complementary color angles equals 90 degrees, consequently if we know the measure of one slant, then we can find the unknown angle easily.

For case, if one of the two angles is 45 degrees, then ;

x + 45 = 90

x = 90 – 45 = 45°

### What is the complementary angle of 40 degrees?

The complementary color lean of 40 degrees is :

90 – 40 = 50 degrees

### How to find supplementary angles?

To find the angle which is auxiliary to another angle, subtract the given lean from 180 degrees.

For example, if one slant is 60 degrees, then another slant is 180 – 60 = 120 degrees .